Please answer all parts of question. i\'ll give A+ Rating 4. (25 pts) You operat

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Please answer all parts of question. i'll give A+ Rating

4. (25 pts) You operate a sushi bar which is the only one in your neighborhood. You estimated that the marginal cost is 10 cents per sushi unit. You know also that each consumer has a demand for sushi given by q-20- 10p, where q is number of sushi units and p is price in dollars per unit. (a) Determine the optimal price per sushi unit and calculate your profit. (5 pts) (b) You are considering switching to an all-you-can-eat-sushi policy. Determine the optimal price per customer. How does profit compare to pricing per unit? (5 pts) (c) Discuss advantages and disadvantages of the all-you-can-eat policy. (5 pts) d) Find what is the optimal two-part tariff for sushi (i.e., a fee at the door plus a price per sushi piece) and calculate your profit. (5 pts) (e) Compare the all-you-can-eat policy with the two-part tariff policy. Which policy may be better? (5 pts)

Explanation / Answer

a) For optimal price we first need to find the inverse demand function given by

q= 20-10p

10p = 20-q

p= 2-0.1q which is the inverse demand function

Since this is the case of monopoly ie there is only one bar in the neighbourhood of sushi , we can simply equate the MR and MC which is the condition for the equilibrium

pq= total revenue = 2q-0.1q2 . By applying the first order condition of differentiation we can find MR from total revenue .

MR= 2-0.2q

Also we are given MC= 0.10 ie 10 cents

Equationg MR and MC we get

2-0.2q=0.1

=> 1.90 = 0.2q

=> q= 9.5

putting value of q in the demand function we get p

p= 2-0.1q = 2-0.1(9.5) = 1.05

profit is given by total revenue- total cost

Total revenue = PQ=1.05* 9.5 = 9.975

Total cost is MC*q = 0.10*9.5= 0.95

Profit = 9.975-0.95= $9.025

b) All you can eat means that the price per unit would be 0 dollars

Putting it in the demand equation we get

q= 20-10(0) = 20

so in a way there is consumer surplus of $20 ie the revenue they can charge from a consumer is $20 .

Now for calculating the profit from this , we can find the total cost which is MC*q = 0.10*20 units = $2

The profit given by this is $20-$2= $18

So this means that if the all you can eat sushi policy($18) earns almost the double of what the owner was earning otherwise .($9.025)

c) All you can eat policy means that after paying an entrance fee or some fixed cost , the consumer can eat in as much amount as he wants ( similar to buffet)

The advantage of this can be that it can be served to large number of consumers so more benefits could be reaped . And since all of them are paying the same fixed cost , the ones who eat less balance out the ones who eat more.

So in a way less food is wasted than the conventional system of dining .

A disadvantage could be that possibly most of consumers who dine at all you can eat are the ones who eat more and so there could actually be losses than gain in such a case.

d) In optimal two price tariff the price is set equal to the marginal cost and the consumer surplus is set as the fees at the door, same as we did in part b but with different values

So the qunatity ordered by each consumer could simply be found be putting the MC in place of price in the demand equation and we get

q= 20-10(0.1) =20 -1 = 19

the consumer surplus is given by the triangle which is the area between the demand curve and the price line

So area is 1/2*b*h= 1/2*19*2-0.10= 1/2*19*1.9 = 18.05

in two part tariff profit is given by

profit = Fixed fee + revenue (pq)- cost (MC*q)

Fixed fee we know is given by consumer surplus and since the pq= MCq as MC=p as we had stated above , Profit is the fixed cost ie $18.05.

e) The profit in all you can eat was $18 while in two part tarriff is $18.05 ie there is difference of 5 cents . So in a way two part tariff is better than all you can eat is a better policy even when the profit difference is less.

( comment for doubts )

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