A firm’s production function is given by q = min{M, L1/2}, where M is the number of machines and L is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit.   a. Is this technology decreasing return to scale? Show your argument. b. Is it true the statement that if average production cost is increasing, a firm’s technology exhibits the decreasing return to scale. (If yes, show the proof. If not, show a counter example) c. Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)

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.

Consider the following short run cost function: TC = 4Q³ - 24Q² + 16Q + 100 Derive the expressions for marginal cost and average total cost. What can we infer about the range of output over which production shows increasing returns to labor and diminishing returns to labor?

The manager of a T-shirt stand found that the cost to produce 10 T-shirts is $105.68, while the cost to produce 40 T-shirts is $402.98. Assume the cost​ C(x) is a linear function of​ x, the number of T-shirts produced. Calculate the marginal cost of a T-shirt, that is, the change in cost of producing one additional T-shirt. (Round to 2 decimal places)

A small clothing manufacturer employs a production method that is approximated by the following production function: q=12KL², where L measures the number of labor hours and K measures the number of rental hours for the machines used in the clothing construction process. Does this production process exhibit increasing, decreasing, or constant returns to scale? Briefly explain your answer. The hourly wage rate for workers at this company is $15; and the rental cost on the machines is $75 per hour. The company has a total budget of $3,150 that it can allocate to cover weekly production costs. The goal of the company's owner is to maximize their output, subject to the constraint of their production budget. Determine the output-maximizing levels of labor and capital the owner will employ.

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.)

Consider the following cost function. a. Find the average cost and marginal cost functions. C(x) = 1700 + 0.4x, 1700 +0.4. a. The average cost function is C(x) = The marginal cost function is C'(x) = 0.4|.

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

Suppose the production function for T-shirts can be represented as q =  L0.25 K0.75. Show that the production function has constant returns to scale.