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Jin Ramen is a restaurant on Broadway. Jin Ramen’s daily Total Costs is TC =q^2/100 +...

Jin Ramen is a restaurant on Broadway. Jin Ramen’s daily Total Costs is TC =q^2/100 + 20q + 400. Where q is the number of meals served each day.

In the evening, customers are willing to pay up to $25 for a meal, while at lunch they do not want to spend more than $15. Should the restaurant remain open for business at lunch-time? Why?

If the restaurant wants to maximize profits, how many meals should it serve each day?

Is the market for restaurant meals around Broadway in long run equilibrium? Why?

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Answer #1

a) It should not open In order to sell in the day time it compares AVC with the pricing. Let q = 1, then AVC = (q^2/100 + 20q)/q = q/100 + 20 = 20.01 which is greater than $15. Hence the price is less than AVC whne q = 1 so it should open in the evening only

b) MC = 2q/100 + 20 and Price is $25. Hence the production rule is P = MC or 25 = 2q/100 + 20

5 = 2q/100

q* = 500/2 = 250 meals per day.

c) Long run has ATC = MC. We have ATC = (q^2/100 + 20q + 400)/q = q/100 + 20 + 400/q and MC = q/50 + 20. Hence we have

q/100 + 20 + 400/q = q/50 + 20

q/50 - q/100 = 400/q

q/100 = 400/q

q^2 = 40000 or q = 200.

Long run equilibrium quantity is 200 so the current equilibrium of 250 is short run equilibrium and not a long run equilibrium.  

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