A. A consumer's utiltiy function for goods and y is U(x, y) = x+y. She has $30 of income and the price of good x is $2 while the price of good y is $3. 1. Graph this consumer's budget constraint. 2. Graph this consumer's indifference curves at Ū = 5, Ū = 10, and Ū = 15. 3. What is this consumer's optimal consumption bundle?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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can all of these please be solved, take all the time that you need.

**E. Perfect Competition**

1. Please explain why the marginal revenue curve for a perfectly competitive firm is horizontal.

2. Suppose a firm is making positive profit in a perfectly competitive market. Use whatever graphs you deem necessary, discuss how this industry will moves toward long run equilibrium.

3. Suppose a firm is making negative profit in a perfectly competitive market. Use whatever graphs you deem necessary, discuss how this industry will moves toward long run equilibrium.

4. In the long run, perfectly competitive firms make zero economic profit. If this is the case, why does the firm even bother producing? Why not exit the market completely?

**F. Highgarden**

Highgarden was the seat of House Tyrell and is the regional capital of the Reach, which is the most fertile part of Westeros, supplying the rest of the realm (especially King’s Landing) with grain, fruit, wine, and livestock. Such large-scale agriculture industry has led to a competitive fertilizer market. Suppose the market for fertilizer in the Reach is perfectly competitive. Firms in the market are producing at their profit-maximizing output but are currently incurring economic losses.

1. How does the price of fertilizer compare to the average total cost and the marginal cost of producing fertilizer?

2. Draw two graphs, side by side, illustrating the present situation for the typical firm and for the market as a whole.

3. Assuming there is no change in either demand or the firms’ cost curves, how will the market adjust in the long run? Explain what will happen in the long run to the price of fertilizer, marginal cost, average total cost, the quantity supplied by each firm, and the total quantity supplied to the market.
Transcribed Image Text:**E. Perfect Competition** 1. Please explain why the marginal revenue curve for a perfectly competitive firm is horizontal. 2. Suppose a firm is making positive profit in a perfectly competitive market. Use whatever graphs you deem necessary, discuss how this industry will moves toward long run equilibrium. 3. Suppose a firm is making negative profit in a perfectly competitive market. Use whatever graphs you deem necessary, discuss how this industry will moves toward long run equilibrium. 4. In the long run, perfectly competitive firms make zero economic profit. If this is the case, why does the firm even bother producing? Why not exit the market completely? **F. Highgarden** Highgarden was the seat of House Tyrell and is the regional capital of the Reach, which is the most fertile part of Westeros, supplying the rest of the realm (especially King’s Landing) with grain, fruit, wine, and livestock. Such large-scale agriculture industry has led to a competitive fertilizer market. Suppose the market for fertilizer in the Reach is perfectly competitive. Firms in the market are producing at their profit-maximizing output but are currently incurring economic losses. 1. How does the price of fertilizer compare to the average total cost and the marginal cost of producing fertilizer? 2. Draw two graphs, side by side, illustrating the present situation for the typical firm and for the market as a whole. 3. Assuming there is no change in either demand or the firms’ cost curves, how will the market adjust in the long run? Explain what will happen in the long run to the price of fertilizer, marginal cost, average total cost, the quantity supplied by each firm, and the total quantity supplied to the market.
**Problem Set 4**

**A.** A consumer’s utility function for goods \( x \) and \( y \) is \( U(x, y) = x + y \). She has $30 of income and the price of good \( x \) is $2 while the price of good \( y \) is $3.

1. **Graph this consumer’s budget constraint.**

2. **Graph this consumer’s indifference curves at \( \overline{U} = 5 \), \( \overline{U} = 10 \), and \( \overline{U} = 15 \).**

3. **What is this consumer’s optimal consumption bundle?**

4. **For this consumer, how are goods \( x \) and \( y \) related? Why does this make sense?**

**B.** As we showed in class, an interior optimal consumption bundle occurs when the indifference curve is tangent to the budget constraint, meaning the two curves have the same slope, thus the marginal rate of substitution is equal to the price ratio of the two goods. This implies that

\[
\frac{MU_1}{P_1} = \frac{MU_2}{P_2}
\]

In words, please describe why this condition must be true.

**C.** As we showed in class, a firm’s profit-maximizing production occurs when marginal revenue is equal to marginal cost.

1. **Discuss what would happen if the firm is producing at a quantity where \( MR > MC \). What can the firm do to raise profit? Explain your reasoning.**

2. **Discuss what would happen if the firm is producing at a quantity where \( MR < MC \). What can the firm do to raise profit? Explain your reasoning.**

**D.** The Airbus A350, first entered service in January 2015 with Qatar Airways, is one of the most technologically advanced passenger airplanes today. Made largely of carbon fibre reinforced polymer, its high fuel efficiency makes it a popular choice of long-range airliner for airlines. Suppose Airbus’ production function for this plane is \( C = 20 + 5Q^2 \), and the plane is sold at a price of \( P = $50 \).

1. **Create a table detailing Airbus’ total cost, average total cost, marginal cost, total revenue, marginal revenue, and profit for each quantity between 0 and 10 of
Transcribed Image Text:**Problem Set 4** **A.** A consumer’s utility function for goods \( x \) and \( y \) is \( U(x, y) = x + y \). She has $30 of income and the price of good \( x \) is $2 while the price of good \( y \) is $3. 1. **Graph this consumer’s budget constraint.** 2. **Graph this consumer’s indifference curves at \( \overline{U} = 5 \), \( \overline{U} = 10 \), and \( \overline{U} = 15 \).** 3. **What is this consumer’s optimal consumption bundle?** 4. **For this consumer, how are goods \( x \) and \( y \) related? Why does this make sense?** **B.** As we showed in class, an interior optimal consumption bundle occurs when the indifference curve is tangent to the budget constraint, meaning the two curves have the same slope, thus the marginal rate of substitution is equal to the price ratio of the two goods. This implies that \[ \frac{MU_1}{P_1} = \frac{MU_2}{P_2} \] In words, please describe why this condition must be true. **C.** As we showed in class, a firm’s profit-maximizing production occurs when marginal revenue is equal to marginal cost. 1. **Discuss what would happen if the firm is producing at a quantity where \( MR > MC \). What can the firm do to raise profit? Explain your reasoning.** 2. **Discuss what would happen if the firm is producing at a quantity where \( MR < MC \). What can the firm do to raise profit? Explain your reasoning.** **D.** The Airbus A350, first entered service in January 2015 with Qatar Airways, is one of the most technologically advanced passenger airplanes today. Made largely of carbon fibre reinforced polymer, its high fuel efficiency makes it a popular choice of long-range airliner for airlines. Suppose Airbus’ production function for this plane is \( C = 20 + 5Q^2 \), and the plane is sold at a price of \( P = $50 \). 1. **Create a table detailing Airbus’ total cost, average total cost, marginal cost, total revenue, marginal revenue, and profit for each quantity between 0 and 10 of
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