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?

Consider a short run production function q = cL+ K where the value for c = 3, using L units of labour and K units of capital. a) Compute the marginal product of labour. b) Does the production function exhibit decreasing, increasing or constant returns to scale? With a diagram. Note: The writing is clear and abbreviations are not allowed.

Suppose that corns are produced according to the production function q = 100K + 50L, where q represents pounds of corns produced per hour, K is the number of acres of land devoted to corn production, and L represents the number of workers hired each hour. 1. Does this production function exhibit increasing, constant, or decreasing returns to scale? 2. Give one reason why this production function is probably not a very reasonable one.

Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.

Suppose a firm has the following production function  Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8  = (16/Q)+ 4√?  (b) Draw the SRAC curve(c) By solving the first order conditions that the global minimum of production is 4(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.

A firm's short-run production function is displayed in the figure below. The firm's variable input is labor. Assume that when Əq (L) 4 units of labor are being used, the slope of the short-run production function reaches its maximum value of 7 (i.e. ƏL 7 when L = 4). As the level of labor increases beyond L = 4, the short-run production function is always becoming less Əq (L) steep (i.e. it is concave). The slope of the production function is equal to 5 when L = 5 (i.e. = 5 when L = 5). If 6 units ƏL Əq (L) of labor are being used, the slope of the production function is 3 (i.e. = 3 when L = 6). If the firm has to pay a wage ƏL of $15 (w = 15) for each unit of labor and can sell each unit of output at a price of $3 (p = 3), what is the firm's profit- maximizing level of output (q) in the short-run? 9₁ 18 14 8 0 4 5 6 q(L) L 7 / 8

Consider a production function Q = (K.5 + L.5) 2    Does this production function exhibit Increasing, Constant, or Decreasing returns to scale?

68. In a perfectly competitive market, industry demand is given by Q = 1000 – 20P. The typical firm’s average cost is TC = 300 + Q2 /3, and marginal cost by MC = (2/3)Q. What is the market price? A.$40 B. $32 C. $28.57 D. $30

Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?

Given the following production function: q = 10KL. Assume that w = 25, r = 75 and C = 1200. (a) Mathematically find the minimum cost combination of capital and labour to produce a given level of output.b) Does the production function in part (a) show increasing returns to scale, decreasing returns to scale, or constant returns to scale? Explain.  (c) Using isoquants and isocosts, graphically illustrate the effect of an increase in the wage rate, assuming the firm is producing at the same level of output.