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 to find the profit-maximizing quantity (Q)

A competitive firm's production function is given by y = f(K, L) = 8K 1/2 + L 1/4 Assume that the price of the good produced is p = $100, the price of capital is r = $4, and the price of labor is w = $5. Find the profit- maximizing levels of capital and labor (K * and L * ). Find the profit-maximizing level of output (y * ). What is the maximum profit of the firm (π * )?

3. Consider a firm that produces a single output Q using two inputs, q₁ and production technology is the Cobb-Douglas: Q = 9tq². 2 - Let pi be the price of q1, and p2 be the price of q2. Assume that the price of the output Q is 1. (b) Find the effect of an input price p2 change on the optimal quantity, q2, of the input good 2 using the implicit function theorem.

Given the information presented in the following graph, which of the following is an accurate statement? Price Po 0 ATC AVC m 20 MC DD Quantity Because this is a perfectly competitive firm, the profit maximizing rule is not P = MC, Profits will be reduced by expanding production to the zone where MC exceeds MR. Because this is a perfectly competitive firm, the profit maximizing rule is not P = MR. Production should keep expanding because MR is always less than MC.

At Bob’s Burgers, each burger consists of exactly two buns x, one meat patty y, and one slice of cheese z. Let P denote the price of burgers and px, py, pz be the prices of each input and consider Bob’s profit maximization problem. (a) Write Bob’s production function q = f(x, y, z), show that it exhibits constant returns to scale, and find the marginal products to each factor. (b) Set up Bob’s cost minimization problem, write the Lagrangian L, and show why you cannot use the first order conditions to solve it. (c) (10) Solve for Bob’s cost function C(q), and find the average cost AC(q) and marginal cost MC(q) functions.

Suppose that r= w=$1 and p= $4. What is the profit maximizing level of output y?

The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 20 1.00 25 2.00 1.20 30 2.46 1.41 35 3.51 1.71 40 4.11 2.01 45 5.43 2.39 50 5.99 2.75 55 8.47 3.27 Instructions: In part a, enter your answer as the closest given whole number. In parts b-d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? pairs b. At the profit-maximizing quantity, what is the total cost of producing ear buds? 2$ c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what will Buddies profit or loss be per week? 2$

On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results.   Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________.   Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.

3. A firm has a production function given by 1 1 A) y = 4x³x² ; 1 1 B) y = 3x4x² ; a) What are the factor demand functions? b) What are the conditional factor demand functions? c) What is the cost function? d) What is the supply function? 1 1 C) y = 5x³x2; 11 D) y = 12xx².

4. For production functions i) q = K0.25L0.25, ii) q = K0.5L0.5, iii) q = KL a) Assume w= $20 and v = $20, what are the long-run MC and AC equations? b) Tum the MC functions into firmlong-run supply equations. c) Graph the MC and AC functions. Assume that the price of output is $20, explain how the q = = q(p = $20) might or might not be a profit-maximizing outcome and whether the SOC's will be satisfied.