A logging operation needs 4 worker-hours (L) per 2 crane-hours (K) to move one batch of a hundred logs in an hour.
Write down the total cost function for the firm (as a function of K and L), given that the hourly wage (w) is $12 and the lease on the crane (r) is $48 an hour. The firm paid $5000 to have the right to log the area.
Graph one isocost line with (K) in the vertical axis. Identify which is more expensive. What is the slope of the isocost line? (be aware of which input is in the vertical axis)
Write down the production function for the logging company, where the output is the number of batches of hundred logs moved per hour.
Graph one isoquant for this production function.
What is the (numeric value) Marginal Rate of Technical Substitution? (again, be aware of which input is asked to be in the vertical axis)
Does this firm’s production function display increasing, constant or decreasing returns to scale?
Suppose that the firm wants to minimize their total cost while being able to move y ̅ (where y ̅ is some – generic – number) batches of one hundred logs an hour: how many cranes and how many workers would it use?
Write down the firm’s total cost (TC), variable cost (VC) and fixed cost (FC) functions, as a function of y. In one plot graph the firm’s TC,VC and FC.
Write down the firm’s average total cost (ATC), average variable cost (AVC), average fixed cost (AFC), and marginal cost (MC) functions, as a function of y. In one plot, graph the ATC, AVC, AFC and MC.
While traveling abroad, Carolina spends all the money in her purse to buy bowls of udon and pieces of sushi. A bowl of udon costs 120 yen whereas a single piece of sushi is 30 yen. Carolina has 720 yen in her purse. Let 𝑢 denote the number of bowls of udon and 𝑠 denote the number of pieces of sushi.
2.1. Write down Carolina’s budget constraint.
2.2. Graph the budget constraint. Please put the number of bowls of udon on the vertical axis.
2.3. What is the slope of the budget constraint?
Suppose Carolina’s preferences can be represented by 𝑣(𝑢, 𝑠) = 6𝑢 + 𝑠.
2.4. Graph two indifference curves for Carolina. Please put the number of bowls of udon on the vertical axis.
2.5. Identify two bundles among which Carolina is indifferent.
2.6. What is Carolina’s Marginal Rate of Substitution?
2.7. What is Carolina’s demand for udon given the current prices and her income?
2.8. What is Carolina’s demand for sushi pieces given the current prices and her income?
2.9. In one graph, depict Carolina’s budget constraint, and two indifference curves, one of which must correspond to her optimal consumption bundle. Identify the optimal consumption bundle.
Suppose that the price of a bowl of udon raises to 240.
2.10. What is Carolina’s demand for udon given the new prices and her income?
Using Slutzky’s decomposition, 2.11. How much of the change in her demand for udon is due to the substitution effect and income effect?
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