Answer to Question #135525 in Microeconomics for Yogita

Question

Suppose the daily demand function for pizza is Qd=1525-5p. For One pizza store the variable cost of making q pizza per day is c(q)=3q+0.01q2,there is a 100 dollar factor cost and the marginal cost =3+0.2q..there is free entry in the long term run.

A.what is the long run equilibrium in market?
B.the fixed cost decrease to 81 dollar?
C.the marginal cost rise 5 dollar per pizza?

Answer 1

A.what is the long run equilibrium in market?

Marginal cost = 3 + 0.2Q

Total cost = $3Q + 0.2Q^2+100$

Qd = 1525 – 5p

p = $\frac{1525-Qd}{5}$

p = 305 – 0.2q

Equilibrium

P = MC

P= Marginal cost = Average total cost = $3+ 0.2q+\frac{100}{q}$

305 – 0.2q = $3+ 0.2q+\frac{100}{q}$

$0.4q + \frac{100}{q} – 302 = 0$

$0.4q^2 – 302q + 100 = 0$

q² – 755q + 250 = 0

Solving the quadratic formula to get q

Q = $377.5 + 22.5\times16.76305$

Q = 377.5 + 377.1686 = 754.6686

Q = 377.5 - 377.1686 = 0.3314

p = 305 – 0.2q

p = $305 – 0.2\times754.6686$

when $q = 754.6686; p = 305 – 150.9337 = 154.0663$

when $q = 0.3314; p = 305 – 0.2\times0.3314 = 304.9337$

B.the fixed cost decrease to 81 dollar?

When fixed cost = 81

TC = $3Q + 0.2Q^2+81$

Solving the equation to get long term equilibrium

P= MC = ATC = $3+ 0.2q+\frac{81}{q}$

305 – 0.2q = $3+ 0.2q+\frac{81}{q}$

q² – 755q + 202.5 = 0

Solving the quadratic formula to get q

Q = $377.5 + 0.5\times754.4634$ = 754.7317

P = $305 – 0.2\times754.7317$ = 154.0537

Q = $377.5 - 0.5\times754.4634$ = 0.2683

P = $305 – 0.2\times0.2683$ = 304.9463

C.the marginal cost rise 5 dollar per pizza?

Marginal cost (MC) = $5

MC = 3 + 0.2Q = 5

Q = 10

TC = $3Q + 0.2Q^2+100$

Since Price = Marginal Cost = Average Cost = 5

Hence: P = MC = AC = 5

Price = 5

P = 305 – 0.2q

5 = 305 – 0.2q

Q = $\frac{300}{0.2}$ = 1500