1
THE COPPERBELT UNIVERSITY
SCHOOL OF BUSINESS
BSP 110 PRINCIPLES OF ECONOMICS
2015 ASSIGNMENT
DUE DATE: 4th January 2016 at 10am
QUESTION
A manufacturing firm in Kitwe has a normal demand curve given by Q = 5,000 – 100P and its total cost curve in the relevant range is TC = 10,000 + 10Q (in K’000).
(i) Over this relevant range, plot the demand curve, marginal revenue curve, marginal cost curve, and average cost curve on one graph paper. Curves should be clearly labelled. (12 Marks)
(ii) Use the above curves to determine the firm’s normal profit-maximising price, quantity, and the amount of profits. (6 Marks)
(iii) Now suppose that there is a temporary shift in monthly demand to Q = 6,000 – 100P. Calculate the firm’s profit when it changes both price and quantity in response to the new demand. Assume the cost of changing prices is K3,000 (this includes the cost of re-adjusting price when ‘normal’ demand conditions return the following month).
(10 Marks)
(iv) Suppose that instead of changing price, the firm adopted a ‘sticky price’ policy and simply let quantity adjust to clear the market. Determine the firm’s profit under this strategy. (6 Marks)
(v) Now consider a short-run fall in monthly demand to Q = 4,000 – 100P. Calculate the firm’s profits when both price and quantity are adjusted in response to the new demand conditions. (Again the cost of changing prices is K3,000. (8 Marks)
(vi) Compare your answer in part (ii) to the level of profits the firm would obtain by adopting a sticky price strategy in the face of the fall in demand. Is the sticky price strategy worthwhile? (8 Marks)
To answer this question, we need to go through the steps and calculations involved. Let's break it down step by step:
(i) Plotting the demand curve, marginal revenue curve, marginal cost curve, and average cost curve:
1. Start with the demand curve equation: Q = 5,000 – 100P. This represents the quantity demanded at each price level.
2. To find the marginal revenue curve, take the derivative of the demand equation with respect to quantity (Q) and multiply it by (-1). Marginal revenue = d(TR)/dQ = d(Q*P)/dQ = P - dP/dQ * Q.
3. The marginal cost (MC) curve is given by the total cost curve (TC) equation: TC = 10,000 + 10Q. To find MC, take the derivative of TC with respect to quantity (Q).
4. The average cost (AC) curve is given by AC = TC / Q.
(ii) Determine the firm's profit-maximizing price, quantity, and amount of profits:
1. The profit-maximizing quantity is where marginal revenue equals marginal cost (MR = MC). Set the MR equation obtained in step 2 equal to the MC equation obtained in step 3 and solve for Q.
2. Substitute the obtained Q value back into the demand curve equation to find the corresponding price (P).
3. Calculate the total revenue (TR) by multiplying the price (P) obtained in step 2 by the quantity (Q) obtained in step 1.
4. Calculate the total cost (TC) using the TC equation given in the question.
5. Calculate the profit by subtracting TC from TR.
(iii) Calculate the firm's profit when changing both price and quantity in response to the new demand:
1. Repeat steps 1-4 from part (ii) using the new demand equation: Q = 6,000 – 100P.
2. Calculate the profit by subtracting TC (including the cost of changing prices, K3,000) from TR.
(iv) Determine the firm's profit under the "sticky price" policy:
1. Calculate the quantity (Q) that clears the market by setting the new demand equation equal to MC: Q = 4,000 - 100P (new demand equation from part v).
2. Calculate the price (P) by substituting the obtained Q value into the new demand equation.
3. Calculate the profit by subtracting TC from TR.
(v) Calculate the firm's profit when both price and quantity adjust in response to the new demand conditions:
1. Repeat steps 1-4 from part (ii) using the new demand equation: Q = 4,000 – 100P.
2. Calculate the profit by subtracting TC (including the cost of changing prices, K3,000) from TR.
(vi) Compare the level of profits obtained in part (ii) to the level of profits obtained under the "sticky price" strategy:
1. Compare the profits obtained in part (ii) to the profits obtained in part (iv) and determine if the sticky price strategy is worthwhile based on the comparison.
By following these steps and performing the necessary calculations, you should be able to answer each part of the question.