PART 1
Question 1
If the price elasticity of demand for firm X’s product is -1.75, lowering its price will result in an increase in total revenue. This is because a negative price elasticity of demand implies an inverse relationship between price and quantity demanded. It indicates that an increase in price leads to a decline in quantity demanded and a decline in price leads to an increase in quantity demanded. In addition, the price elasticity of demand is more than 1 in absolute terms hence a change in price leads to a more than proportionate change in quantity demanded. A 1% decrease in the price of firm X’s product will therefore lead to a 1.75% increase in quantity demanded. The demand for the product is therefore price elastic hence a decrease in price will lead to a large increase in quantity demanded and hence an increase in total revenue.
Question 2
Marginal cost refers to the cost incurred for an additional unit of output. Marginal cost function is given by differentiating the total cost function.
TC = 1,000 + 18Q + 3Q3
MC = ∂TC∂Q = 18 + 9Q2
For fifth unit, Q = 5
Therefore, MC = 18 + 9 × 52
MC = 18 + 225
MC = 243
Question 3
Profit is usually the difference between total revenue earned in a given period and total cost incurred to generate that revenue. The major difference between accounting and economic profits is what constitutes total cost. In the case of accounting profit, total cost includes only explicit costs. Explicit costs are those costs that involve the direct payment of resources/money such as cost of raw materials, cost of labour and other expenses. On the other hand, economic profit is the difference between total revenue and total cost, which includes both explicit and implicit costs. Implicit costs include the opportunity cost of factors of production owned by the firm. Opportunity cost is the value of the option sacrificed in order to achieve a given objective. This difference is explained by the illustration below.
An agricultural firm grows coffee in a given piece of land and earns an annual revenue of £20,000 from the sale of coffee and incurs an annual total cost of £15,000. The same piece of land could be used to grow beans from which the firm could earn a total revenue of £3,200. In this case, accounting profit will be £5,000 (20,000 – 15,000) while economic profit will be £1,800 (20,000 – [15,000 + 3,200]). When opportunity/implicit costs are positive, accounting profit will be higher than economic profit. On the other hand, if implicit costs are negative, economic profit will be more than accounting profit.
Question 4
This is a two-tailed test hence Z = 1.96
Confidence interval for a:
= 250 ± [1.96 × 15]
= 250 ± 29.4
= (220.6, 279.4)
Confidence interval for b:
= 15 ± [1.96 × 0.75]
= 15 ± 1.47
= (13.53, 16.47)
Question 5
Cross price elasticity of demand is the change in quantity demanded of a commodity resulting from a unit change in the price of a related commodity, substitute or complimentary.
XEDPB = ∂QP∂QB = 3.5
∂QP-0.03 = 3.5
∂QP = - 0.03 × 3.5
= - 0.105
If the price of peanut butter decreases by 3%, there will be a 10.5% decline in the quantity demanded of bananas. This is because the two commodities are substitutes as indicated by the positive cross price elasticity of demand. A decrease in the price of one leads to a decline in quantity demanded of the other. A decrease in the price of peanut butter will make it cheaper than bananas hence some consumers will switch their consumption from bananas to peanut butter.
Question 6
The present value of the cash flows is $7,392.29.
Question 7
Qh = 100 – 8Ph + 6Pb – M
Ph = $4, Pb = $2 and M = $10
Qh = 100 – [8 × 4] + [6 × 2] – M
= 100 – 32 + 12 – 10
= 70
Cross price elasticity of demand between beer and hot dogs = ∂Qh∂Pb × PBQh
= +6 × 270
= 0.1714
PART 2
Question 1
The demand equation given can be used to formulate policies that would increase sales. From the demand function, it is clear that the quantity demanded of good X is inversely related to the price of good X. The company can therefore increase its sales by reducing the price of good X. The company should also increase the amount of advertising expenditure on good X. As indicated by the demand function, the coefficient of advertising expenditure on good X is positive hence an increase in advertising expenditure on X will lead to an increase in its quantity demanded. An increase in income could also lead to an increase in the company’s sales but the company has no control over that. In addition, a reduction in the price of commodity Y and advertising expenditure on good Y will result in an increase in quantity demanded of X. However, the company has no control over these variables. The best the company can do is to adjust the variables it has control over. For instance, the company can reduce the price of good X if the price of good Y is increased. The company can also increase its advertising expenditure if that of good Y is increased.
Question 2
Forecasting the amount of sales for the next 12 quarters would require the estimation of a demand equation. In this case, total sales for previous periods will be collected. In addition, data on factors affecting demand for the product such as the commodity’s price, prices of other related goods, income of consumers, advertising expenditure, among other data. The data will then be used to determine the regression equation of the demand for the commodity. In addition, time series and trend analysis will be conducted for each variable to predict their values for each of the 12 quarters. With the predicted values of the variables and the demand equation, quarterly slaes will be determined.
Question 3
Value of the firm, PV (firm) = P0 × 1+ii-g
Where P0 is the current profit, I is the interest rate and g is the profit growth rate
Value of the firm = 100,000,000 × 1+0.70.07-0.05
= 100,000,000 × 53.5
= $5,350,000,000
Since the profit growth rate, g is less than the interest rate, i, paying out dividends will decrease the value of the firm.
Question 4
Knowledge of elasticity is helpful to a business manager in a number of ways. Firstly, price elasticity of demand enables the manager to assess the impact of changes in prices of its commodity and other related commodities. It enables the manager to determine the impact of a proposed change in price on the total revenue of the business thus ensuring sound pricing decisions are made. In addition, knowledge of price elasticity of demand helps in price discrimination if a business is selling its products in different markets with distinct features. Revenue will be maximised if price is lowered in a market where the demand for the commodity is elastic. In markets where the demand for the commodity is price inelastic, revenues can be maximised by increasing the price of the commodity. Elasticity of demand also allows a business manager to assess the impact of shifting the burden of taxation to the consumer. This assists the manager to react appropriately to changes in taxation of commodities sold by the business.
Knowledge of elasticity also helps a business manager to determine the effects of changes in price, among other factors, on the supply of a commodity. Any business purchases commodities, either raw materials or finished goods. Elasticity enables a manager to determine the right time for purchasing in order to lower production costs for the business. For instance, if the supply of a raw material is supply elastic, a reduction in its price may lead to future shortages which in turn results in higher prices. In such a case, the business manager should purchase large quantities of the raw material to avoid paying more in future.
Question 5
The burning of coffee bean crop results in a decline in the supply of coffee and the supply curve shifts inwards as shown below. This results in a decline in quantity demanded of coffee since it becomes more expensive than tea.
Price S2
S1
P2
P1
D
Q2 Q1 Quantity
In the above diagram, a reduction in the supply of coffee leads to a reduction in equilibrium quantity and an increase in equilibrium price of P1 to P2.
An increase in the equilibrium price of coffee will lead to an increase in quantity demanded of tea since both commodities are substitutes. This leads to outward shift in the demand curve for tea as shown in the diagram below. Other factors held constant, an outward shift in demand curve will lead to an increase in both equilibrium price and quantity of tea. Bumper harvest of tea in India leads to an increase in the quantity supplied of tea. The supply curve therefore shifts outwards. This in turn leads to an increase in equilibrium quantity but a reduction in equilibrium price. The net effect of the two changes is an increase in equilibrium quantity as shown below. However, the change in equilibrium price will depend on the magnitude of the change in the two factors. An increase in the price of coffee leads to an increase in demand for tea which raises the price of tea. However, an increase in the supply of tea results in a decline in the equilibrium price of tea. If the cross-price elasticity of demand between coffee and tea is higher than elasticity of supply then the net effect will be an increase in equilibrium price.
S1
Price S2
P1
P2
Pe
D2
D1
Qe Q1 Q2 Quantity
In the diagram above, a shift in demand curve from D1 to D1 leads to an increase in price from Pe to P1 and equilibrium quantity from Qe to Q1. An outward shift in supply curve from S1 to S2 further increases equilibrium quantity from Q1 to Q2 and reduces equilibrium price from P1 to P2.
Question 6
CED of kielbasa and sauerkraut = ∂ in quantity of sauerkraut∂ in price of kielbasa × Initial price of kielbasainitial quantity ofsauerkraut
= 40-4 × 8100
= -10 × 0.08
= - 0.8
This implies that a 1% change in price of kielbasa leads to a change in quantity demanded of sauerkraut by 0.8%. Since the cross-price elasticity of the two goods is positive, the two goods are substitutes. For substitute goods, the change in quantity demanded of good 1 and the change in price of good 2 moves in the same direction.
Question 7
An indifference curve is a locus of points showing all combinations of two goods that yield the same amount of satisfaction/utility to the consumers.
Characteristics of indifference curves
- Indifference curves slope downwards from left to right. This is because if a consumer uses good X and Y, then to maintain utility after reducing the quantity of Y, the consumer has to consumer more units of X.
- Indifference curves are convex to the origin. This is because if a consumer has more units of a good, he/she will give up more units of the good to acquire units of the other good.
- Where there are more indifference curves, the higher indifference curve indicates the preferred combination.
- Indifference curves do not intersect each other.
PART 3
Question 1
- QD = 5 - 0.5P, QS = 0.5P – 1
At equilibrium, QD = QS
Therefore, 5 – 0.5P = 0.5P – 1
-P = -6
Pe = 6
QD = 5 – [0.5 × 6] = 5 – 3 = 2
- Inverse demand function:
Qd = 5 – 0.5P
0.5P = 5 – Qd
P = 10 – 2Qd
- Consumer surplus = 12 × Qe × [Pmax – Pe]
Pmax ids the price at which the quantity demanded is 0
Pmax = 10
Consumer surplus = 12 × 2 × [10 – 6] = 4
- An increase in the price of the commodity will decrease since it will reduce the difference between the maximum price consumers are willing to pay and the equilibrium price. The larger the difference between equilibrium price and the maximum price consumers are willing tpo pay, the larger the consumer equilibrium.
Question 2
- Cost function, C = 6Y2, Benefit function, B = 400Y – 2Y2
Marginal Cost, MC = ∂TC∂Q = 12Y
Marginal benefit, MB = ∂TB∂Q = 400 – 4Y
- At equilibrium, MC = MB
400 – 4Y = 12Y
Y = 25
The level that maximises net benefit is 25.
- Maximum level of benefit = 400 – 4 (25)
= 400 – 100
= 300
- The use of marginal analysis helps the manager to determine the output level that maximises net benefits/profit. In addition, marginal analysis also helps in assessing the incremental effect of a proposed decision.
Question 3
- Equation of the budget line: 25S + 5I = 300
- Graph of Sara’s budget constraint
Question 4
- Regression equation:
Average test score = 636.08 + 0.05X1 + 13.82X2 + 1.48X3 – 0.48X4
Where X1 is student-teacher ratio, X2 is number of computers per student, X3 is average income and X4 is the percentage of English learners.
- Average test score = 636.08 + 0.05[16] + 13.82[0.2] + 1.48[89] – 0.48[0.2]
= 636.08 + 0.8 + 2.764 + 131.72 – 0.096
= 771.268
- This regression equation provides a good model for estimating average test score. This can be indicated by the high Adjusted R Square of 0.706. This implies that 70.6% of changes in average test score are explained by changes in the independent variables. This is good enough since only about 30% of changes in average test score are not explained by variables not included in the model. In addition the standard error (10.32) is low hence the model is good. In addition, the F-Significance for the model is far much lower than 0.05 hence we can conclude that the model is statistically significant.
