A gadget-making firm is engaged in long-run production plann…

A gadget-making firm is engaged in long-run production planning.  They must first decide whether to make a small investment (for a fixed cost of $20), or a large investment (for a fixed cost of $40).  After this decision, the firm decides how many gadgets to produce: 1, 2, or 3.  The total variable costs for a small investment firm are: $25 if one gadget is produced.  $60 if two are produced.  $85 if three are produced. The total variable costs for a large investment firm are: $0 if one gadget is produced.  $30 if two are produced.  $50 if three are produced. If the firm seeks to minimize average total costs here, should they make the small or large investment?   (Type either “small” or “large” here, without the quotes.)  How many gadgets do they produce?   At what average total cost? $ per gadget.

Carl opens a shop to produce widgets.  He must decide how ma…

Carl opens a shop to produce widgets.  He must decide how many workers to employ, each of whom are able to produce some number of widgets.  We provide the total number of widgets sold for every possible number of workers in a list here:   # of workers total widgets produced 1 6 2 11 3 15 4 18 5 20 6 21   Notice that production here obeys the law of diminishing marginal product.  Widgets are sold at a market price of $3 each.  Carl must pay each worker employed $5 for their labor.  To maximize profits, how many workers does Carl hire?   Total profits are $. Now say that wages go up to $7.  How many workers does Carl hire now?   Total profits are $. Finally, say that wages are set at $13.  How many workers does Carl hire?   Total profits are $.

Carl has $20, which he’d like to spend on some combination o…

Carl has $20, which he’d like to spend on some combination of coconuts and pineapples.  His goal is to maximize utility from consumption — we provide here his total utility for coconut and pineapple consumption:   coconuts pineapples quantity total utility quantity total utility 1 60 1 80 2 112 2 144 3 156 3 192 4 196 4 224 5 228 5 240   Carl’s total utility is the sum of his utility from consuming coconuts and his utility from consuming pineapples.  Coconuts cost $4 each.  First, say that pineapples cost $8 each.  If so, how many coconuts does Carl purchase?   How many pineapples?   What is his total utility? Say that the grocery store discounts pineapples to $4 each.  Solve the problem again.  How many coconuts does Carl purchase now?   How many pineapples?   What is his total utility?