Suppose that a firm's production function is: Its marginal product functions are: q=101050.5 112 98- 84- MP| = 5K05,L05 = 0.5ql. and MPK = 5L0.5/0.5 = 0.5q/K. The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require 56.00 units of labor. (Enter your response rounded to two decimal places.) K If the marginal rate of technical substitution is find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is units. (Enter your responses as integers.) <, Units of capital 70- 56- 42- 28- 14- 4-280 140 0- 0 14 28 42 56 70 84 98 112 L, Units of labor

Suppose a pizza parlor has the following production costs: $5.00 in labor per pizza, $3.00 in ingredients per pizza, $0.20 in electricity per pizza, $1,500 in restaurant rent per month, and $250 in insurance per month. Assume the pizza parlor produces 1,000 pizzas per month. What is the variable cost of production (per month)? The variable cost of production is $ (Enter your response as an integer.) What is the fixed cost of production (per month)? The fixed cost of production is $ ☐. (Enter your response as an integer.)

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?   $20 $10 $50 $100

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?