1. Consider a firm which produces according to the following production function by using labor and capital: f (k,l) = = min (5k, 10l) a. Find firm's long run total cost function given that price of capital is v and price of labor is w. I b. Find marginal cost and average cost functions and draw them on a graph.

Suppose Z=0, Y=9. Please solve in details.

Emma sells hot chocolate outside of Yankees baseball games. They have two inputs in the production of hot chocolate: (hot chocolate mix (x1, measured in kg) and labour (x2, measured in hours. The production function for hot chocolate (in liters) is: f (x1 , x2) = (x1)1/3(x2)1/3 A) Does this firm have constant, increasing or decreasing returns to scale? The cost of hot chocolate mix is w1, and the cost of labour is w2. If Emma produces "y" liters of hot chocolate the cheapest way possible, then B) How many kilograms of hot chocolate mix would they use? C) How many hours of labour? D) What is the cost function of producing this much hot chocolate?

Cost curves in the long run differ from cost curves in the short run.   This is true right.

Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use two gumball presses and one worker to produce 1,000 gumballs per hour. a. Explain why the cost per hour of producing 1,000 gumballs is 2v + w (where v is the hourly rent for gumball presses and w is the hourly wage). b. Assume Acme can produce any number of gumballs they want using this technology. Explain why the cost function in this case would be TC = q(2v +w), where q is output of gumballs per hour, measured in thousands of gumballs. c. What is the average and marginal cost of gumball production (again, measure output in thousands of gumballs)? (show the complete formula) Draw the graph for the average and marginal cost curves for gumballs assuming v=3, w-5 (show working) Now draw the graph for these curves for  v=6, w=5.( show working) Explain why these curves have shifted.

K A cereal factory has weekly fixed costs of $22,000. It costs $1.26 to produce each box of cereal. A box of cereal sells for $4.06. Find the rule of the cost function c(x) that gives the total weekly cost of producing x boxes of cereal. OA. c(x)=1.26x OB. c(x)=22,000+ 1.26x OC. c(x)=22,000 +4.06x OD. c(x)=22,000+ 2.8x

Explain the relationship between the production function and the average costs and marginal costs curve of a firm.

The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d)  Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e)  Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?

A firm's production function is given by Q = 20L0.8 K0.2. At that moment, the firm sets = 1,000 and K = 1,000. Which of the following combinations of L and Klies on the same isoquant? L = 1,063.9; K = 698.7 L= 1,063.9; K = 698.7 L=698.7; K = 1,063.9 L = 1,302.3; K = 936.1 L 936.1; K 1,302.3

Suppose a firm has the following production function Q (K, L) =K0.5 L0.4. Show mathematically whether the firm has increasing, decreasing, or constant returns to scale.