Microeconomics Answers

Suppose a firm operating in a perfectly competitive industry has costs in the short run given by:

SRTC = 8 + 1/2Q^2 and therefore MC = q.

1. (a) Derive expressions for fixed costs (FC), those that do not vary with output, variable costs (VC), those that do vary with output, average variable cost (AVC), and average total cost (ATC).
2. (b) At what quantity is AVC at its minimum (at what AVC level)? At what quantity is ATC at its minimum (at what ATC level)? Calculate ATC at q = 2 and q = 8 and sketch MC, AVC and ATC betweenq=0andq=8.

If income elasticity of demand of good X is 0.89, what will happen to equilibrium price if there is an increase in income of consumers? Draw a diagram to support your answer. 

If income elasticity of demand of good X is 0.89, what will happen to equilibrium price if there is an increase in income of consumers? Draw a diagram to support your answer. 

If Road Transport Authority (RTA) UAE increases the bus-fare from Abu Dhabi to Dubai, then what will happen to their revenue? [Hint: the demand curve is inelastic] Explain your answer with help of a diagram

Describe how one may use the Median Voter Theorem to derive a demand curve for a public good. Also discuss the problems that may arise and the solutions to these in implementing this procedure.

Andrew, Beth and Cathy live in Lindhville. Andrew’s demand for bike paths, a public good, is given by Q=12-P. Beth’s demand is Q=18-P and Cathy’s is Q=8-(P/3) The marginal cost of building (a kilo-meter of path) is MC=$21.

(a)      Find the socially desirable (Pareto Efficient) amount of bike paths (in kilo-meters).

(b)      What is the total cost of building the amount bike paths you found in (a).

(c)      How would government charge the individuals to cover its costs (i.e., how much each individual be charged for a unit bike path and how much each of them will end up paying in total.

If Veronica Vaughn spends all of her daily income on cigarettes and Yoo Hoo, she can afford 10 packs of cigarettes and 10 bottles of Yoo Hoo. She can also afford 6 packs of cigarettes and 22 bottles of Yoo Hoo.

(a)  What is the relative price of cigarettes in terms of bottles of Yoo-Hoo (i.e, what is the ratio of prices, Pc/Py?)

(b)  Exactly how much income does Veronica earn in one week if the price of cigarettes is $6? Write a budget equation for Veronica that is a function of the pack of cigarettes, C, and the number of bottles of Yoo Hoo, Y.

(c)  Draw veronica’s daily budget set with packs of cigarettes on the x-axis and bottles of Yoo Hoo on the y-axis.

Consider a firm's profit function, II(x) = R(2) -C(2), where R(x) is total revenue as a function of output (2), and C(x) is total cost as a function of output

(a) Under perfect competition, each firm is a price taker. Assuming a competitive market price, p* = 10 and a cost function, C(x) = (x – 5), express the firm's profit as a function of x.

(b) Find the competitive firm's profit maximizing level of output, r* (Hint: maximize the firm's profit by taking the first derivative of the profit function, setting it equal to zero, and solving for the level of output, r*).

(c) If the firm were only interested in minimizing costs, what level of output would it choose?

Question 2

Table 1 below shows Troy’s consumption choices of three goods. Each observation consists of a set of prices and quantity consumed of the three goods. [25%]

Table 1

Observation 𝑝1 𝑝2 𝑝3 𝑥1 𝑥2 𝑥3 1332844 2212486 3414248

Note: The prices are in dollars and the quantities are in units.

a. Write a table containing the total expenditure of each bundle under each set of prices. List all the affordable bundles at each set of prices.

b. Refer to the table in (a). List all the direct and indirect revealed preferences and explain whether the data satisfies the WARP and SARP.

c. Usethetablein(a)toexplainwhatyouunderstandaboutthetwoproperties of strict order.

d. Suppose that Troy now consumes only good 1 and good 2. The prices and quantities consumed of the two goods remain unchanged for the three observations in Table 1. Sketch a diagram to explain whether WARP and SARP is violated.

Jose consumes only good A and good B. His utility function is C (A, B) = 4AB + 20. The price of good A is $4, but if Jose consumes more than 10 units of good A, the price is $1 higher. The price of good B is constant at $2 and his income is constant at $400. [25%]

a. Formulate Jose’s budget constraint and explain how his budget set changes when he consumes more than 10 units of good A.

b. Refer to the budget constraint in (a). Explain how Jose’s optimal choice and wellbeing change.

c. What other strategies that the government could use to control the consumption of good A? Use a diagram or a budget constraint function to explain one strategy.

d. Does the policy in (c) make Jose worse off? Discuss.