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1. Consider the market for apartments in Atlanta. Suppose that the supply and demand curves in this unregulated competitive market are given by: P= 12- QD P = 2+ Qs a. What is the equilibrium price and quantity in this market? b. Sketch a graph of this market and label the consumer surplus and producer surplus. c. Calculate the consumer surplus and producer surplus. Now suppose that the city government implements a price ceiling of $4. d What is the quantity of apartment supplied at a price of $4? e What is the quantity demanded at a price of $4? f. Sketch a graph of this market with the price ceiling and label the new consumer surplus and the new producer surplus.Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which can be combined to produce Y units of output according to the following production function: Y = 30K + 10L 7. Suppose the firm can choose whatever combination of capital (K ) and labor (L) it wants to produce 600 units. Suppose the price of capital is $1,000 per machine per week. What combination of inputs (K and L) will the firm use if the weekly salary of each worker is $400?Problem 4 - Optimal production The Acme Corp produces widgets using labor (L) and capital (K) according to the production, Q = F(L, K) = LI/4K1/4. A widget sells at price P = 16. A unit of labor costs W = 1 and a unit of capital costs R = 4. In the short run, the firm's capital is fixed at K = 1/2 and only labor can be set freely. In the long run, both capital and labor can be chosen freely. There are no fixed costs. 1. In the short run, if Acme Corp wants to produce an output level. Q, solve for its labor demand, LSR(Q). 2. Using your expression for LSR(Q), solve for the firm's short run cost function, CS#(Q). 3. Solve for the short run marginal cost function, ACS?(Q). With this, find Aeme's optimal short run output level OSH 1. In the long run. Acme can change both capital and labor as it pleases. Find the optimal long run capital and labor input choices for a given output level, Q. Denote the optimal long Fun input choices by L(Q) and K (Q). State the long run cost function C(Q) 5. Determine Acme's optimal output choice in the long run, Q. How much labor does Acme demand in the long run. L"? Compare with your answer to question 3. Explain the differencethat the following production function is given: ( - min(-, L.) a-) (6 points) For the above production function, find the elasticity of substitution? Find the Returns to Scale. b.) (8 points) Using the above production function: find the labor demand and capital demand as functions of output (Q). price of labor (w) and price of capital (r). Does the Law of Demand hold for each input? Are these inputs normal or inferior inputs in the production process? Are inputs complements or substitutes? Why? e-) (10 points) Find the cost function for the above production function. Verify the properties of the cost function d-) (8 points) Suppose that a firm wants to produce 36 units of output and w=1, 1=1. Find long run total cost. Suppose now that wage goes up to 2. Find the new long run total cost. Does firm substitute capital for labor? What is the percentage of cost saving relative to the case where firm is not able to substitute? e-) (4 points) Suppose that w-1, 1-1 and a firm has fixed amount of capital K - 108 in short nim (SR) Find the short run total cost, average total cost and marginal cost. What would be the short run total cost of producing 36 units, Compare your answer with long run total cost in part d. How and why are they different