Econ 1302 Midterm II Practice Problems PDF

Econ 1302: Midterm II Practice Problems SOLUTIONS This is a set of practice problems to help in preparation for the coming exam. Work through each question carefully, and make note of any difficulties or misunderstandings you have. We will be reviewing these questions in the class prior to the exam...

Econ 1302: Midterm II Practice Problems SOLUTIONS This is a set of practice problems to help in preparation for the coming exam. Work through each question carefully, and make note of any difficulties or misunderstandings you have. We will be reviewing these questions in the class prior to the exam date. Please come with questions so that you and your fellow students can best prepare. Producer Theory I 1. In microeconomics, we assume that the goal of the consumer is to maximize utility. What is the corresponding goal of the firm? Goal of the firm is to maximize profit. 2. What is a production function? What is its purpose for understanding the behavior of the firm? A production function is a mathematical relationship that expresses how much output can be produced with a given amount of inputs. This relationship implicitly can be described as: q = f (X) where q is output quantity, and X is a set of inputs. Under the basic case, we assume firms produce q with inputs of labor L and capital K. The (implicit) production function is thus: q = f (L, K) The production function is critical for the theory of the firm, as it expresses the physical engineering requirements of production. 3. Figure 1 displays an isoquant. In a few words, what does an isoquant represent? An isoquant represents all the possible combinations of labor and capital that can be used to produce a given level of output. 4. Explain the concept of marginal productivity. Marginal Productivity refers to the additional output generated from using one more unit of a particular input while keeping other inputs constant. In other words, it measures how much extra product is produced when an additional unit of labor, capital, or another resource is employed. 5. Explain the concept of diminishing marginal productivity. Diminishing marginal productivity is a principle stating that as more units of an input are added, while other inputs remain fixed, the additional output produced from each 1  new unit of input will eventually decrease. For example, if a farmer keeps adding workers to a fixed-sized field, each new worker might initially contribute a lot to the harvest. However, as more workers are added, they may get in each other’s way or run out of tools, leading to less additional output from each new worker. This concept is analogous to diminishing marginal utility for the consumer. 6. Explain the di↵erence between the short-run and the long-run as we define them in microeconomics. The short-run is defined as the period of time in which a firm can change its level of output only by varying its variable inputs. Variable inputs are inputs that can be changed quickly (i.e. labor, raw materials, some types of tools). The long-run is the period of time where the firm can vary all of its inputs, both labor and capital, to adjust output. 7. A common simplifying assumption in producer theory is that labor is a variable input and capital is a fixed input. How do we justify this assumption? In what circumstances may this assumption not hold? This assumption is justified by the observation that while a firm can hire or fire workers on a daily/weekly/monthly basis, many types of capital take significant amounts of time to introduce. For example, a firm cannot add a new factory or storefront to increase output on a daily or weekly basis. This assumption may not hold when we consider that many types of labor require significant amounts of time to hire, onboard, train, etc., making them less flexible than assumed. Similarly, some forms of capital (raw materials, small tools, etc.) can easily be varied on a short-run basis. Producer Theory II 8. What are fixed costs? Variable costs? Total costs? Marginal costs? Average total costs? For each, explain in words as well as their equation definition. Variable cost (VC): cost of variable inputs Fixed cost (FC): cost of fixed inputs Total cost (TC): fixed cost plus variable cost TC = V C + FC Marginal cost (MC): cost of producing one more additional unit of output TC MC = q Average total cost (ATC): total cost divided by total output TC AT C = q 2  9. What does diminishing marginal productivity imply for variable cost (in the short- run)? The notion of diminishing marginal productivity of labor suggests that while con- tinuing to add labor to the production process will continue to increase output, it will do so at a smaller and smaller amount. Diminishing marginal productivity of labor suggests that in order for a firm to increase its output in the short-run, it will need to hire increasingly more labor for higher levels of output. This leads to exponentially growing variable cost (and total cost). 10. Suppose a firm has a fixed cost of $100, and its variable costs are given by q 2. In Figure 2, sketch the firm’s fixed, variable, and total cost functions. Make sure to label the y-intercept, and identify two points on the total cost curve with their corresponding y and x values. Finally, be sure to identify which curve corresponds to which function. 11. What is perfect competition? What are the four necessary conditions for perfect competition to occur? Perfect competition occurs when there is a market where all firms are price takers in both the input markets and output market. In other words, the firms experience perfectly elastic demand in the output market, and perfectly elastic supply in the input markets. This occurs when the following conditions are true:... Products are identical Consumers have full information on all prices Consumers enjoy low transaction (shopping) costs There is free entry exit of firms in the market 12. Consider the market for apartments in NYC. Is this market perfectly competitive? If so, how does it satisfy the necessary conditions? If not, which conditions are violated? No. Products are not identical (many di↵erent types of apartments). There is also not free entry into the market, as there is significant regulation on becoming a landlord in NYC. Consumers generally have close to full information on prices and relatively low shopping costs (online platforms). 13. What is profit? What is the profit maximizing condition? What is the profit maxi- mizing condition under perfect competition? Profits are total revenue minus total cost: ⇡ = TR TC Profit maximizing condition states that any firm seeking to maximize profit will pro- duce a level of output q ⇤ such that marginal revenue is equal to marginal cost: MR = MC Under perfect competition, marginal revenue is always equal to the market price, and thus the profit maximizing condition under perfect competition is P = MC 3 14. Suppose a firm is operating under perfect competition, and exhibits diminishing marginal productivity from all variable inputs. Finally, suppose there is a non-zero level of out- put for which the firm can earn positive profit. (a) Sketch total revenue and total costs in Figure 3. Identify the the level of output (roughly) where the firm is maximizing its profits. Label this q ⇤. (b) Suppose now the price of q falls such that the firm cannot earn positive profit. Draw this change in Figure 3. (c) What will the firm do in the short-run if profits are negative? What will it do in the long-run? Note: your answer for the short-run should include a conditional statement such as “if revenue is greater than...”. In the long-run, a firm will always shut down if profits are negative. In the short- run, the firm will continue to produce if total revenue is greater than its variable cost TR > V C as this allows the firm to recoup some of its fixed cost in the short-run. If revenue is less than variable cost, the firm will shut down in the short-run. 4 Figures Figure 1: An isoquant 5  2 = 100 + 9 TC = FC + vc = $93 vc $136 - -- - - - -. i $125....... ↑ ↑ : & FC = $100 : ~ ! $36.. I -- -. - $25-... --- 5 Figure 2: Fixed costs, variable costs, total costs 6  TC TR o * Decline in Price * W TR i , ↑ firm is now - unprofitable : (UT50 for all values of. : q) I q Figure 3: Total revenue vs. total cost 7