ECON 356
Homework Assignment Five
Due Thursday, Nov. 18
Directions: Copy and paste this into a word document and then type your answers. Graphs do not have to be typed - BUT please leave space for your graphs on your answer sheet. Do not use a separate piece of paper.
(40 pts.)
1. Suppose the marginal product of labor is currently equal to its average product and both are 2 units per hour and the good produced is sold for $10 per unit. If you were the marginal worker hired to this firm and your marginal product is higher than the last person hired, would you prefer to be paid the value of your average product (after you are hired obviously) or the value of your marginal product? Explain your answer by using an example with numbers - use the numbers given in the problem and then make up any additional numbers you might need to make your point. (Hint: to find the value of your marginal or average product in $ terms - simply multiply the marginal or average product by the price the output is sold for - per unit. So if the average and marginal product is 2 per hour, and each unit is sold for $10, then the value of the product to the firm is $20 per hour). (5 pts.)
2. Draw a short run production function and then explain why it is shaped the way it is shaped. (4 pts.)
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3. Diminishing marginal returns relates to the short run, while decreasing returns to scale relates to the long run. Explain why. (4 pts.)
4. Suppose that 5 units of capital and 3 units of labor are initially used in production. Now suppose that the input combination is changed so that 2 units of capital and 8 units of labor are used to produce the same level of output.
a. Graph this situation on an isoquant curve. (4 pts.)
b. Calculate the marginal rate of technical substitution (for every decrease in one unit of capital, how many units of labor are required to produce the same output)?
Show all work. (3 pts.)
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5. Draw an isocost line for the following information: total expenditures or cost = $30,000. Price of labor = $15 and the price of capital = $25. Then redraw the isocost line on the same graph with this one change: the cost of capital decreases to $20. Put all appropriate numbers on your graph. (4 pts.)
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6. If the wage = $3 and the cost of capital = $6, draw the isocost lines that correspond to total expenditure of $90 and $180 and $270 per unit of time. Label all numbers. (4 pts.)
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7. Now draw isoquant curves tangent to your isocost lines and derive your long run output expansion path (on the same graph above). (2 pts.)
8. Assume a firm is in the short run. It's price (which is charged for all of its output sold) = $35.00 per unit. It is currently selling an output of 120 units. Its total variable costs are $2400. Its total fixed costs are $2000. Since this firm is losing money, it is thinking about shutting down. Should it shut down? Explain your answer -- make sure you show numbers!! (4 pts.)
9. Statement one: the firm will operate (to max profit or min loss) at the output level where MR = MC AND Statement two: the firm will shut down in the short run if its price does not cover its AVC. Explain both in words and graphically how the short run supply curve (relationship between price and quantity supplied) for a firm in the perfectly competitive model is derived. Make sure you explain why and how both the statements above relate to your answer. (6 pts.)
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