Question

Consider a continuum of consumers distributed along a line of length 100. Each consumer buys one unit of the good. There are two firms, one located at each end of the line. For simplicity, assume that firm A is located at 0 while firm B is located at 100. Firm A’s mill price is pA and firm B’s mill price is pB.

A consumer located at x buying from firm A pays a full price of: pA +  .

A consumer located at x buying from firm B pays a full price of: pB +  ,

where t > 0 is a parameter measuring transportation costs and x ∈ [0, 100]. For simplicity, assume that the marginal cost of production is constant and given by c > 0. Firms choose prices simultaneously.

1. Identify the marginal consumer and obtain the system of demand functions facing these firms. Briefly discuss your results.

2. Write down the payoff functions and obtain the system of best-response functions. Are firms’ prices strategic substitutes or strategic complements? Briefly discuss the intuition behind your result (maximum 100 words).

3. Solve the system of best-response functions to find the Nash equilibrium prices, quantities and profits. In light of your results, briefly discuss whether the following statement is correct: ’If firms were able to, they would reduce consumers’ transportation costs t to zero.’

4. Now assume that firm A operates at a marginal cost of 25 and firm B operates at a marginal cost of 50. Everything else remains the same. Explain whether the following statement is correct (maximum 200 words): ’Firm A will obtain higher profits than firm B in equilibrium because even though both firm A and B sell to half of the market in equilibrium, firm A will be able to charge higher prices because of its competitive advantage.

(e)

Now assume that in a stage prior to price competition, the two firms can endogenously choose where to locate along the line. The location decisions are taken simultaneously. By the time they choose prices, they know each other’s locations. For simplicity assume that firm A locates at a distance a from 0 and firm B at a distance b from 100 and that c = 0 for both firms. Everything else remains the same as above.

What is the most appropriate game-theoretic solution concept to use for this game? Justify your answer

Derive the solution to this game, explaining the method that you have followed and discussing the implications of your result in terms of product differentiation

Consider a continuum of consumers distributed along a line of length 100. Each consumer buys one unit of the good. There are two firms, one located at each end of the line. For simplicity, assume that firm A is located at 0 while firm B is located at 100. Firm A’s mill price is pA and firm B’s mill price is pB.

A consumer located at x buying from firm A pays a full price of: pA +  .

A consumer located at x buying from firm B pays a full price of: pB +  ,

where t > 0 is a parameter measuring transportation costs and x ∈ [0, 100]. For simplicity, assume that the marginal cost of production is constant and given by c > 0. Firms choose prices simultaneously.

1. Identify the marginal consumer and obtain the system of demand functions facing these firms. Briefly discuss your results.

2. Write down the payoff functions and obtain the system of best-response functions. Are firms’ prices strategic substitutes or strategic complements? Briefly discuss the intuition behind your result (maximum 100 words).

3. Solve the system of best-response functions to find the Nash equilibrium prices, quantities and profits. In light of your results, briefly discuss whether the following statement is correct: ’If firms were able to, they would reduce consumers’ transportation costs t to zero.’

4. Now assume that firm A operates at a marginal cost of 25 and firm B operates at a marginal cost of 50. Everything else remains the same. Explain whether the following statement is correct (maximum 200 words): ’Firm A will obtain higher profits than firm B in equilibrium because even though both firm A and B sell to half of the market in equilibrium, firm A will be able to charge higher prices because of its competitive advantage.

(e)

Now assume that in a stage prior to price competition, the two firms can endogenously choose where to locate along the line. The location decisions are taken simultaneously. By the time they choose prices, they know each other’s locations. For simplicity assume that firm A locates at a distance a from 0 and firm B at a distance b from 100 and that c = 0 for both firms. Everything else remains the same as above.

What is the most appropriate game-theoretic solution concept to use for this game? Justify your answer

Derive the solution to this game, explaining the method that you have followed and discussing the implications of your result in terms of product differentiation

Consider a continuum of consumers distributed along a line of length 100. Each consumer buys one unit of the good. There are two firms, one located at each end of the line. For simplicity, assume that firm A is located at 0 while firm B is located at 100. Firm A’s mill price is pA and firm B’s mill price is pB.

A consumer located at x buying from firm A pays a full price of: pA +  .

A consumer located at x buying from firm B pays a full price of: pB +  ,

where t > 0 is a parameter measuring transportation costs and x ∈ [0, 100]. For simplicity, assume that the marginal cost of production is constant and given by c > 0. Firms choose prices simultaneously.

1. Identify the marginal consumer and obtain the system of demand functions facing these firms. Briefly discuss your results.

2. Write down the payoff functions and obtain the system of best-response functions. Are firms’ prices strategic substitutes or strategic complements? Briefly discuss the intuition behind your result (maximum 100 words).

3. Solve the system of best-response functions to find the Nash equilibrium prices, quantities and profits. In light of your results, briefly discuss whether the following statement is correct: ’If firms were able to, they would reduce consumers’ transportation costs t to zero.’

4. Now assume that firm A operates at a marginal cost of 25 and firm B operates at a marginal cost of 50. Everything else remains the same. Explain whether the following statement is correct (maximum 200 words): ’Firm A will obtain higher profits than firm B in equilibrium because even though both firm A and B sell to half of the market in equilibrium, firm A will be able to charge higher prices because of its competitive advantage.

Answer 1

Answer

Request calendars can be attracted up to show how a solitary individual responds to valu request bend will be determined by including the total of every individual purchaser in a market

The connection between cost and amount requested is the beginning stage for building a model of purchaser conduct. Estimating this relationship gives data that is utilized to make an interest function* and request plan, from which an interesting bend can be inferred. When an interesting bend has been made, different determinants can be added to the model.

An interesting plan shows the amount that would be requested at various speculative costs and can be determined from real marketing projections, or from statistical surveying. For instance, the timetable depends on an overview of understudies who demonstrated what number of jars of cola they would purchase in seven days, at different costs.

Probably the most punctual clarification of the converse connection among cost and amount requested is the law of lessening negligible utility. This law proposes that as all the more an item is expended the minimal (extra) advantage to the buyer falls, thus customers are set up to save money. This can be clarified as follows:

The most advantage is produced by the main unit of a decent expended in light of the fact that it fulfills the vast majority of the quick need or want.

A subsequent unit expended would produce less utility – maybe even zero, given that the purchaser has less need or less want.

With less advantage determined, the discerning shopper is set up to pay fairly less for the second, and ensuing, units, given that the negligible utility falls.

Consider the accompanying figures for utility determined by a person when expending bars of chocolate. While complete utility keeps on ascending from additional utilization, the extra (minor) utility from each bar falls. On the off chance that the minor utility is communicated in a money related structure, the more prominent the amount devoured the less the peripheral utility and the less worth determined – subsequently, the same customer would be set up to save money on that unit.e changes or to show how an entire market will respond to value changes.