Last Updated 22 Jul 2020

# Managerial Economics Solution

Suppose the Singapore government wants to decrease the domestic consumption of cigarettes to 300,000 packs a day and wants to achieve this by imposing a tariff on sacks of cigarettes.

- A. What size tariff will achieve this objective?
- B. What are the amounts of consumer surplus, government revenue, and deadweight loss under this tariff?
- C. Now suppose the Singapore government issues and exclusive license to import cigarettes to one company. What will be the monopoly price and the resulting level of domestic consumption? What are the levels of consumer surplus, producer surplus, and deadweight loss?
- D. Now suppose under this monopoly the Singapore government wishes to reduce the domestic consumption of cigarettes to 300,000 packs per day. What size tariff goes the government needs to impose in this scenario? What is the resulting profit for the monopolists, government revenue, consumer surplus, and deadweight loss?

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**Solutions:**

- a. The Supply curve is perfectly elastic at P=$4, so at P=$4, 50,000 4 800,000. So P=4 and Q = 800,000 Managerial Economics Solution By Johnny's
- b. Domestic consumption is 300,000 when the consumer price Pc satisfies, 300,000 50,000. Or when PC=14. So the Excise tax equals 14-4 = 10. $/q Government Revenue = = 20 CSS = DEL = Excise tax 14 4 1 oho q.
- c. MR. = 20 -q/25, oho MR.=MAC, implies 20 or Or pence found by obstructing the monopoly quantity into the demand curve. 400,000 1 50,000 or porn = 12. CSS = 12 MAC.
- d. Need to find the excise tax that will equate + Excise Tax MAC + tax 8 = 20 = 8 8=4+ tax tax = 4. CSS = 900,000; G. R = 1. 2 million, AS = 1. Million, DEL Saki's utility function for coke (C) and nuts (N) is = 4. Let Pc=4, = 2. 5 million PEN=I , and 1=6. What is Saki's utility maximizing commodity bundle? Next, provide a graph of Saki's income consumption path. (1 5 points).

**Solution:** Here the income expansion path is given by the equation describing the corners of the indifference curves. C The optimal consumption bundle is found where the budget line: **C* + N*** intersects the ICC. By substitution 6 or 6 0. By the quadratic formula N=2. Substitution into the ICC or Budget Line yields C. Suppose the price of a loaf of bread rises by 50%, and the cross-price elasticity of peanut butter with respect to bread is -0. 5. (1 5 points)

- A. If the initial quantity of peanut butter purchased was 10 Jars, what is the new quantity of peanut butter charged after the change in the price of bread?
- B. Now suppose that the total expenditure on peanut butter does not vary with the price of meant butter, what is the own-price elasticity of peanut butter?
- C. If the only two commodities are the bread and peanut butter, given the information in this question, what is the income elasticity of peanut butter?

**Solution: **

- a. So the new quantity purchased is 7. 5
- b. Own price elasticity must be -1
- c. Use the property that the sum of all elasticity equals zero. PEP,price of Bread + PEP, price of BP + PEP,I = O -0. 5+-1 + PEP

**Consider a price-taking firm that is operating in the short-run. (20 points).**

- A. Provide a graph that depicts a scenario in which the optimal decision is to shut down in the worth run.
- B. Provide a graph that depicts a scenario in which the firm earns negative profits in the short run but should continue to produce. On this graph be sure to show the profit-maximizing production level, total revenue, total costs, total variable costs, and fixed costs.
- C. Provide a graph that depicts a scenario in which the firm earns positive economic profits. Be sure to show the profit-maximizing quantity, the level of profits, total costs, and total variable costs. This graph identifies the quantity at which the firm maximizes the average profit per unit (I. E. Margin. Explain why maximizing profit is not the same as maximizing margins.

**Solution:** See Lecture 7. Apt Slides 12, 15, and 18.

Suppose a firm digs tunnels and can use either robot (R) or humans (H) to produce meter lengths of tunnels according to the production function** M(R, H) = OR + AH.** What are the conditional input demand functions for the robots and humans as a function of the number of meters M, price of robots PR, and the price of Human labor MR? = 6 and MPH = 2. So the firm will always choose to use only Robots if PR < 2 PH, only use humans if **PR > 2 PH**, and is indifferent between Robots and Humans if PR = PH. F so 2 if otherwise and The long-run cost function is 6) Suppose the long-run average cost function for producing palm oil is 1 5 20. 10 15 and the long-run marginal cost. Also assumes the market demand for Palm oil is 600,000 15,000. In the long-run competitive equilibrium what is the market price, market quantity, the production level of each firm, and how many firms will produce? (1 5 points) Solution: In the LIRE, P=rant TACT. Or 15 sq or At q* = 15 TACT? 10 which is where the market price converges to. At 600,000 1 5,000 10 450,000 So the number of firms = 450,000/1 5 or 30,000.

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