A firm’s production function is Q = 10 + 30L - .5L2+ 30K – K2, and its competitive demand function is PQ= MRQ = d = $40. The prices of L and K are PL = $6 and PK= $12. Suppose K is fixed at K =10. Use Excel Solver or otherwise to find the profit-maximizing quantity (Q).
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A firm’s production function is Q = 10 + 30L - .5L2+ 30K – K2, and its competitive demand function is PQ= MRQ = d = $40. The prices of L and K are PL = $6 and PK= $12. Suppose K is fixed at K =10. Use Excel Solver or otherwise to find the profit-maximizing quantity (Q).
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- Firm A and Firm B sell identical goods The total market demand is:Q(P) = 1,000-1.0P The inverse demand function is therefore: P(QM) = 10,000-10QM QM is total market production (i.e., combined production of firm’s A and B). That is: QM = QA + QB As a result, the inverse demand curve for each firm is: P(QA,QB) = 10,000-10QA-10QB The difference between this example and the example in class is that the two firms have different costs. Firm A has the same cost as in class, but firm B has a different cost function: TCA(QA) = 5000QA TCB(QB) = 5000QB Using the demand function and the cost functions above, what is firm A’s profit function? Using the profit function above and assuming that firm B produces QB, calculate what firm A’s best response is to firm B’s decision to produce QB. (Note: Firm A’s best response should be a function of QB) Using the demand function and the cost functions above, what is firm B’s profit function? Using the profit function above and assuming that firm A…A competitive firm’s production function is given by y= f(x1,x2)= 4x11/2 + 10x21/2 a) The price of factor 1 is 1, the price of factor 2 is 1, and the price of output is 2. Find the profit-maximizing quantities of x1 and x2? What is the profit-maximizing quantity of output? b) Redo part (a), this time by first deriving the firm’s factor demand functions and the supply function, and then substituting the prices in these functions.Consider two firms that produce a single output good,y, using two inputs :Capital, K , and labor, L, the prices of each unit of capital and labor are r and w,respectively. The output good y sells for $p per unit. Firm A's production function is y = fa(K,L) = K1/4L1/4. The profit function is equals to : K1/4L1/4 - rK -wL. a) FInd the profit maximizing levels of K and L as functions of r,w, and p. b) Suppose that r = w= $1 and p =$4 . What is the profit maximizing level of output,y?
- Consider the following production function for a firm: y=(x1-1)(x2-1), if x1≥1 and x2≥1; and y=0, if either x1<1 or x2<1: Find the firms supply function and verify the law of supply.A competitive firm’s production function is given by y= f(x1,x2)=x1ax2b If a=b=0.5 , the price of factor 1 is 12, and the price of factor 2 is 3, find the cost minimizing input combinations and the total cost of producing 40 units of output. Redo part (1), this time by first deriving the firm’s conditional factor demand functions and the cost function.Say the the aggregate inverse demand function is D(Q) = 100 - Q, where Q = q1+q2. Both firms have the same cost c(q)=cq. Only firm q1 is allowed to participate. Therefore, q2 = 0. Find the function that maximizes welfare. What is the demand and price when welfare is maximized?
- Assume the demand function for a product is given by QD = 20,000 – 10P + 0.4I, where P = price of the product, and I = average income of consumers. Also, assume the supply function of the product is given by QS = 30P. If the market for the product is perfectly competitive, and the average income of consumers is $10,000, what are the equilibrium price and quantity in this market?Assume that a competitive firm has the total cost function: TC=1q3−40q2+880q+2000 T C = 1 q 3 - 40 q 2 + 880 q + 2000 Suppose the price of the firm's output (sold in integer units) is $550 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. How many units should the firm produce to maximize profit? Please specify your answer as an integer. What is the total profit at the optimal output level? Please specify your answer as an integer.(i) If the demand curve for a particular commodity is p = −0.09x + 51 and the total cost function C(x) = 1.32x2 + 11.7x + 101.4,where x is the level of production. Find: 1. All values of x for which production of the commodity is profitable.
- Suppose that the market for apples is perfectly competitive. Production of apples requires two inputs:workers (L) and land (K). The production function for apples is:F(K,L)=3K^(1/3)* L^(2/3) A) Suppose that W=4, R=16, and in the short-run, K=27. Find the firm’s short-run cost function SRC(q)and short-run marginal cost function SRMC(q).B) What is the optimal production of apples if P=4? What are consumer surplus and profit?C) Find the firm’s short-run supply of apples Q(P) when W=4, R=16 and K=27.D) Find the firm’s long-run cost function LRC(q) and long-run marginal cost function LRMC(q) when W=4and R=16. How do these compare to the firm’s short-run cost function and marginal cost function?E) Find the firm’s long-run supply of apples q(P) when W=4 and R=16.Suppose the (inverse) demand for a firm’s product is given by P = 10−2Q and the cost function is C(Q) = 2Q What is the profit-maximizing level of output and price for this firm?Suppose a typical (representative) corn farm has a short run production technology which results in the outcome of U-shaped Average Variable Cost (AVC), Average Total Cost (ATC), and Marginal Cost (MC). Further, suppose this firm sells its product in a market where the price of the good is determined by the interaction of market Demand and Supply. Because an individual firm is very small compared to the rest of the market, we treat the market price as the price given to the firm, and the individual firm cannot impact that price. assume we are in the Short Run for this firm. In graphing, put $ on the vertical axis and lower-case q (firm output) on the horizontal axis. Start with the AFC0, AVC0, ATC0, and MC0 curves . show shifts in any of the cost curves, reflecting the higher cost of land (keeping in mind that this higher cost is independent of how much or how little corn is actually produced) and labeling the changed cost curves with a subscript 1. On the graph with $ on the…
