$1.(10$ points$)$ Profit Maximization with no price discrimination

You are running a $($small$)$ chain of gourmet burger joints with two locations $($San Antonio and Laredo$)$

You have been charging $$12$ for your burger meal $($fries$,$ burger and soft drink$).$ When you add up sales across both locations, you sell $6000$ meals per week at this price

When you raised the price to $$16$ for the burger meal, your combined sales across the two locations fell to $4000$ meals per week.$$

For your costs, you have fixed costs of $$3000$ per week across the two locations. In addition, it costs you$$ six dollars per burger in variable costs $($ingredients$,$ labor etc.$)$

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A$.$ What is your combined cost function across the two locations

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B$.$ Using the two prices above, estimate your combined demand function across the two locations

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C$.$ Using the combined demand function and cost function calculated above, calculate the profit maximizing price and quantity

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D$.$ What are your $($combined$)$ weekly profits across the two locations at the optimal price?

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$2.(10$ points$)$ Profit Maximization with price discrimination

After taking your managerial economics class, you realize that you can probably raise your profits by charging different prices in the two locations $($price discriminating$).$ To work out the optimal price in each city, you breakdown sales across the two locations.

In Laredo:$$ You sold $1200$ burger meals per week at $$12$ and $400$ meals at $$16$

In San Antonio:$$ You sold $4800$ meals per week at $$12$ and $3600$ meals at $$16$

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A$.$ Using the two prices above, estimate your demand function in Laredo

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B$.$ Using the two prices above, estimate your demand function in San Antonio.

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C$.$ What is your cost function in Laredo?

For your costs in Laredo, you have fixed costs of $$1000$ per week. In addition, it costs you six dollars per burger in variable costs $($ingredients$,$ labor etc.$)$

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D$.$ Using the demand function for Laredo that you calculated earlier, calculate the profit maximizing price and quantity for Laredo.$$ Is the new price higher or lower than the price if you do not price discriminate?$$

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E$.$ What are your profits in Laredo?

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F$.$ What is your cost function in San Antonio?

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For your costs in San Antonio, you have fixed costs of $$2000$ per week. In addition, it costs you six dollars per burger in variable costs $($ingredients$,$ labor etc.$)$

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G$.$ Using the demand function for San Antonio from above calculate the profit maximizing price and quantity for San Antonio.$$ Is the new price higher or lower than the price if you do not price discriminate?$$

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H$.$ What are your profits in San Antonio?

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$3.(10$ points$)$ Summary of results

A$.$ Are consumers in Laredo better or worse off with price discrimination or no price discrimination?$$ EXPLAIN

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B$.$ Are consumers in San Antonio better or worse off with price discrimination or no price discrimination?$$ EXPLAIN

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C$.$ Are your firm$$s profits higher or lower with price discrimination?

ANSWER $3$A Please