To determine whether this is a long-run equilibrium and to calculate the profit or loss situation, we first need to find the profit-maximizing level of output and price. 1. First, we need to find the marginal revenue (MR) and marginal cost (MC). The MR is the derivative of the total revenue (TR) with respect to quantity (Q), and the MC is the derivative of the total cost (TC) with respect to Q. 2. The TR is P*Q, where P is the price. Substituting the demand equation into the TR equation, we get TR = (225 - 10Q)*Q = 225Q - 10Q^2. The derivative of this with respect to Q gives us the MR: MR = 225 - 20Q. 3. The TC is given by the cost function, so the MC is the derivative of the cost function with respect to Q: MC = 0.3Q. 4. To find the profit-maximizing level of output, we set MR = MC and solve for Q: 225 - 20Q = 0.3Q. Solving this equation gives us Q = 225/20.3 = 11.08. 5. Substituting Q = 11.08 into the demand equation gives us the price: P = (225 - 10*11.08)/10 = $11.48. 6. The profit is TR - TC. Substituting Q = 11.08 and P = $11.48 into the TR and TC equations gives us TR = $127.15 and TC = $18.34. So, the profit is $108.81. 7. In a long-run equilibrium in monopolistic competition, firms make zero economic profit. Since the profit is positive, this is not a long-run equilibrium. So, the profit or loss situation at this profit-maximizing level of output is a profit of $108.81.

The market structure of the local pizza industry is best characterised by monopolistic competition. Pizza Shack is one of the producers in the local market.The market demand for Pizza Shack is: Qd = 225 – 10P.Pizza Shack’s cost function is: C(Q) = 0.15Q^2Where Q^2 refers to q squaredIs this a long-run equilibrium?9. Calculate the profit or loss situation at this profit maximising level of output: Blank 1. Fill in the blank, read surrounding text.

Question

The market structure of the local pizza industry is best characterised by monopolistic competition. Pizza Shack is one of the producers in the local market.The market demand for Pizza Shack is: Qd = 225 – 10P.Pizza Shack’s cost function is: C(Q) = 0.15Q^2Where Q^2 refers to q squaredIs this a long-run equilibrium?9. Calculate the profit or loss situation at this profit maximising level of output: Blank 1. Fill in the blank, read surrounding text.

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Solution 1

To determine whether this is a long-run equilibrium and to calculate the profit or loss situation, we first need to find the profit-maximizing level of output and price.

First, we need to find the marginal revenue (MR) and marginal cost (MC). The MR is the derivative of the total revenue (TR) with respect to quantity (Q), and the MC is the derivative of the total cost (TC) with respect to Q.
The TR is P*Q, where P is the price. Substituting the demand equation into the TR equation, we get TR = (225 - 10Q)*Q = 225Q - 10Q^2. The derivative of this with respect to Q gives us the MR: MR = 225 - 20Q.
The TC is given by the cost function, so the MC is the derivative of the cost function with respect to Q: MC = 0.3Q.
To find the profit-maximizing level of output, we set MR = MC and solve for Q: 225 - 20Q = 0.3Q. Solving this equation gives us Q = 225/20.3 = 11.08.
Substituting Q = 11.08 into the demand equation gives us the price: P = (225 - 10*11.08)/10 = $11.48.
The profit is TR - TC. Substituting Q = 11.08 and P = $11.48 into the TR and TC equations gives us TR =$ 127.15 and TC = $18.34. So, the profit is$ 108.81.
In a long-run equilibrium in monopolistic competition, firms make zero economic profit. Since the profit is positive, this is not a long-run equilibrium.

So, the profit or loss situation at this profit-maximizing level of output is a profit of $108.81.

This problem has been solved

Solution 2

To determine whether this is a long-run equilibrium and to calculate the profit or loss situation, we first need to find the profit-maximizing level of output.

First, we need to find the price that maximizes profit. To do this, we need to set the derivative of the demand function with respect to price equal to zero and solve for P. The demand function is Qd = 225 - 10P. The derivative of this function with respect to P is -10. Setting this equal to zero and solving for P gives us P = 22.5.
Next, we substitute P = 22.5 into the demand function to find the quantity that maximizes profit. Substituting P = 22.5 into Qd = 225 - 10P gives us Q = 225 - 10(22.5) = 112.5.
Now we can calculate total revenue (TR) and total cost (TC). TR is PQ, so TR = 22.5112.5 = $2531.25. TC is given by the cost function C(Q) = 0.15Q^2, so TC = 0.15(112.5)^2 =$ 2531.25.
Finally, we can calculate profit, which is TR - TC. In this case, profit = $2531.25 -$ 2531.25 = $0.

Since profit is zero, this is a long-run equilibrium. In the long run, firms in monopolistic competition make zero economic profit. If firms were making positive economic profit, more firms would enter the market, increasing supply and driving down prices until profit is zero. If firms were making negative economic profit, some firms would exit the market, decreasing supply and driving up prices until profit is zero.

This problem has been solved

Solution 3

To determine whether this is a long-run equilibrium and to calculate the profit or loss situation, we first need to find the profit-maximizing level of output and price.

First, we need to find the marginal revenue (MR) and marginal cost (MC). The MR is the derivative of the demand function with respect to Q, and the MC is the derivative of the cost function with respect to Q.
The demand function is Qd = 225 - 10P. To express this in terms of Q, we rearrange to get P = 22.5 - 0.1Q. The MR is then the derivative of (P*Q) with respect to Q, which gives MR = 22.5 - 0.2Q.
The cost function is C(Q) = 0.15Q^2. The MC is the derivative of this with respect to Q, which gives MC = 0.3Q.
To find the profit-maximizing level of output, we set MR = MC and solve for Q. This gives 22.5 - 0.2Q = 0.3Q, which simplifies to 0.5Q = 22.5, so Q = 45.
Substituting Q = 45 into the demand function gives P = 22.5 - 0.1*45 = 18.5.
The total revenue (TR) is PQ = 18.545 = 832.5. The total cost (TC) is C(Q) = 0.15*45^2 = 303.75.
The profit is TR - TC = 832.5 - 303.75 = 528.75.
In a long-run equilibrium under monopolistic competition, firms make zero economic profit. Since the profit is positive, this is not a long-run equilibrium.

So, the profit at this profit-maximizing level of output is 528.75, and this is not a long-run equilibrium.

This problem has been solved

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