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What is the long-run total cost function for producing tricycles, TC(Q, PW, PF)? What is the production function for tricycles, Q(F, W )?
Derive the firm's long-run total cost curve and average cost curve in terms of the input prices and Q.
Derive its long-run total cost curve in terms of the input prices, w and r. Verify that if the input prices double, then total cost doubles as well.
Derive the expression for the long-run total cost that the firm incurs, as a function of Q and the factor prices, w and r.
The production function Q = KL+ M has marginal products MPK = L, MPL= K, and MPM = 1. What is the short-run total cost of producing 400 units of output?
Derive expressions for, and then sketch, the corresponding short-run average cost, average variable cost, and average fixed cost curves.
Why would this condition not necessarily hold at a corner point optimal solution?
How does an increase in the price of an input affect the slope of an isocost line?
What would be an example of an implicit cost you would incur in operating this business?
It plans to use these tubes to clone snake cells. Explain why the opportunity cost of using these test tubes might not equal the price at which they were acquir
Show that the innovation has resulted in technological progress in the sense defined in the text.
What can you say about the returns to scale of the Leontief production function Q = min(aK, bL), where a and b are positive constants?
Draw several isoquants of the cake production function. What can you say about returns to scale for this function?
Draw the isoquants for bicycle production. Write a mathematical expression for the production function for bicycles.
Suppose that a firm's production function is given by Q = KL + K, with MPK = L + 1 and MPL = K. Calculate how much labor is required at point B.
What is the marginal rate of technical substitution of labor for capital (MRTSL,K) at any point along an isoquant?
Sketch a graph of the isoquants for this production function. Does this production function have an uneconomic region? Why or why not?
What is the general equation for the isoquant corresponding to any level of output Q? Does isoquant exhibit diminishing marginal rate of technical substitution?
Find marginal products of K and L for each pair of inputs in the table. Then, carefully, sketch several of isoquants associated with this production function.
Suppose K = 600. Find the total product function and graph it over the range. At what level does the marginal product curve appear to reach its maximum?
Why would a firm that seeks to minimize its expenditures on inputs not want to operate on the uneconomic portion of an isoquant?
Why can a total product function exhibit diminishing marginal returns but not diminishing total returns?
At the beginning of the year, before the retailer has purchased any printers, what is the opportunity cost of laser printers?
The firm wants to produce 120 gadgets. What are the cost-minimizing input quantities? Illustrate your answer with a clearly labeled graph.
A cost-minimizing firm's production function is given by Q = LK. What would the cost-minimizing input combination be after the price changes?