Problem 2 The following graphs show the aggregate market and a representative individual firm in industry Y: Aggregate Market Price 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 S with damage cost S without damage cost Damage cost Demand 2,000 4,000 6,000 8,000 10,000 12,000 Quantity Individual Firm Price 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 MSC MC Damage cost D = MR 1 2 3 4 5 6 7 8 9 10 11 12 Quantity
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- In the aggregate market graph, the profit-maximizing quantity is where the supply curve without damage cost (S without damage cost) intersects the demand curve. - From the graph, this intersection occurs at a quantity of 10,000 units. Show more…
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Question 1: Given the following cost function:TC = 1500 + 15Q – 6Q2 + Q3i. Determine the total fixed cost for producing 1000 units of output and 500 units of output.ii. What is AFC at:a) 1000 units of outputb) 500 units of outputiii. Determine TVC, AVC, MC and AC at 50 units of output. Question 2: The demand function equation faced by PTCL for its computers is given by:P = 50,000 – 4Qi. Write the marginal revenue equationii. At what price and quantity marginal revenue will be zero?iii. At what price and quantity will total revenue be maximized? Question 3: Suppose the following demand and supply function:Qd = 750 – 25PQs = -300 + 20 Pi. Find equilibrium price and quantityii. Find consumer and producer surplus Question 4: Given production function:Q = L 3/4 . K1/4Find out the optimal quantities of the two factors using Lagrangian method, if it is given that price of labor is Rs.6 and price of capital is Rs.3 and total cost is equal to Rs.120.Question 5: Given the cost function isTC = 6L + 3KFind out the optimal quantities of the two factor using Lagrangian method, if it is given thatoutput is equal to 13.46 = L3/4 . K1/4 Question 6: Suppose that the production function of the firm is:Q = 100L1/2.K1/2K= 100, P = $1, w = $30 and r = $40. Determine the quantity of labor that the firm should hire in order to maximize the profits. What is the maximum profit of this firm? Question7: Solve the above problem for w = $50. Question 8: Given TC = 100 + 60Q – 12Q2 + Q3Finda. The equations of the TVC, AVC, and MC functions.b. The level of output at which AVC and MC are minimum, and prove that the AVC andMC curves are U-shaped.c. Find the AVC and MC for the level of output at which the AVC curve is minimum. Question 9: Answer the same questions as in the above problem if:TC = 120 + 50Q – 10Q2 + Q3 Question10: If the demand function faced by a firm is:Q = 90 – 2PTC = 2 + 57Q – 8Q2 + Q3Determine the level of output at which the firm maximizes the profit.
Manasvee S.
Assume the following cost data are for a purely competitive producer: $$\begin{array}{ccccc} \hline \begin{array}{c} \text { Total } \\ \text { Product } \end{array} & \begin{array}{c} \text { Average } \\ \text { Fixed cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Variable cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Total cost } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { cost } \end{array} \\ \hline 0 \\ 1 & \$ 60.00 & \$ 45.00 & \$ 105.00 & \$ 45 \\ 2 & 30.00 & 42.50 & 72.50 & 40 \\ 3 & 20.00 & 40.00 & 60.00 & 35 \\ 4 & 15.00 & 37.50 & 52.50 & 30 \\ 5 & 12.00 & 37.00 & 49.00 & 35 \\ 6 & 10.00 & 37.50 & 47.50 & 40 \\ 7 & 8.57 & 38.57 & 47.14 & 45 \\ 8 & 7.50 & 40.63 & 48.13 & 55 \\ 9 & 6.67 & 43.33 & 50.00 & 65 \\ 10 & 6.00 & 46.50 & 52.50 & 75 \\ \hline \end{array}$$ a. At a product price of $\$ 56,$ will this firm produce in the short run? Why or why not? If it is preferable to produce, what will be the profit-maximizing or loss-minimizing output? Explain. What economic profit or loss will the firm realize per unit of output? b. Answer the relevant questions of 4 a assuming product price is $\$ 41$ c. Answer the relevant questions of 4 a assuming product price is $\$ 32$ d. In the table below, complete the short-run supply schedule for the firm (columns 1 and 2 ) and indicate the profit or loss incurred at each output (column 3). $$\begin{array}{cccc} \hline \begin{array}{c} \text { (1) } \\ \text { Price } \end{array} & \begin{array}{c} \text { (2) } \\ \text { Quantity } \\ \text { Supplied, } \\ \text { Single Firm } \end{array} & \begin{array}{c} \text { (3) } \\ \text { Profit }(+) \\ \text { or Loss }(-) \end{array} & \begin{array}{c} \text { (4) } \\ \text { Quantity } \\ \text { Supplied } \\ 1500 \text { Firms } \end{array} \\ \hline \$ 26 & \text {_____} & \$ \text {_____} & \text {_____} \\ 32 & \text {_____} & \text {_____} & \text {_____} \\ 38 & \text {_____} & \text {_____} & \text {_____} \\ 41 & \text {_____} & \text {_____} & \text {_____}\\ 46 & \text {_____} & \text {_____} & \text {_____} \\ 56 & \text {_____} & \text {_____} & \text {_____} \\ 66 & \text {_____} & \text {_____} & \text {_____} \\ \hline \end{array}$$ e. Explain: "That segment of a competitive firm's marginalcost curve that lies above its average-variable-cost curve constitutes the short-run supply curve for the firm." Illustrate graphically. f. Now assume that there are 1500 identical firms in this competitive industry; that is, there are 1500 firms, each of which has the cost data shown in the table. Complete the industry supply schedule (column 4). g. Suppose the market demand data for the product are as follows: $$\begin{array}{|cc|} \hline \text { Price } & \begin{array}{c} \text { Total Quantity } \\ \text { Demanded } \end{array} \\ \hline \$ 26 & 17,000 \\ 32 & 15,000 \\ 38 & 13,500 \\ 41 & 12,000 \\ 46 & 10,500 \\ 56 & 9500 \\ 66 & 8000 \\ \hline \end{array}$$ What will be the equilibrium price? What will be the equilibrium output for the industry? For each firm? What will profit or loss be per unit? Per firm? Will this industry expand or contract in the long run?
Question 5: (12 marks) Part A: (4 marks) Consider a concert hall that seats 400 people. The concert organizers are aware that there are two different market segments. One is for regular adults defined by P1 = 600 - Q1. The other is for students and senior citizens defined by P2 = 400 - Q2. For the sake of convenience, we will assume that all costs are fixed, such that the marginal cost of each additional audience member is zero. This implies that maximizing profit is the same as maximizing revenue. The concert organizers wish to maximize profit (revenue) but can do so with the constraint that only 400 tickets can be sold. This means that the concert organizers are not able to independently maximize profit (revenue) in each market segment because that might mean having to sell more than 400 tickets. How many tickets should be sold in each market segment and at what price in each segment to maximize profit (revenue)? Part B: (8 marks) Consider a monopolist who sells in two different markets. The (inverse) demand curve in Market 1 is given by P1 = 360 - Q1. The (inverse) demand curve in Market 2 is given by P2 = 240 - Q2. For the sake of convenience, we will assume that the monopolist has zero marginal costs implying that maximizing profit and maximining revenue are synonymous for this monopolist. (i) What is the revenue-maximizing quantity and price in Market 1? What is the resulting revenue? (2 marks) (ii) What is the revenue-maximizing quantity and price in Market 2? What is the resulting revenue? (2 marks) (iii) Now suppose the monopolist did not discriminate in prices and charged the same price in both markets. What is the revenue maximizing price and quantity in this case? Show that the resulting revenue is less than what the monopolist makes when she charges two different prices across the two different markets. (4 marks)
Akash M.
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