Chapter 9, Competitive Firms Video Solutions, Intermediate Microeconomics: A Tool-Building Approach

Problem 1

Daniel Archer's Midland farm produces corn. His cost function (where total cost is measured in cents) is calculated to be
$$
c(q)=\frac{q^3}{480}-\frac{q^2}{2}+100 q+1000,
$$
where $q$ is the output level (measured in bushels). The market price of corn is 220 cents per bushel which Midland farm, as a competitive producer, takes as given. How many bushels will Daniel produce? What is Midland farm's shutdown price?

Jonathan Tapiwa

Numerade Educator

04:56

Problem 2

In the market for manhole covers, there are 120 identical firms, each firm having the cost function $c(q)=0.5 q^2+4 q+18$, where $q$ is the number of manhole covers produced by each firm. The market demand curve is given by $Q^d(p)=1720-100 p$.
(a) Calculate the shutdown price, $p_{s d}$ of a typical firm.
(b) Derive a typical firm's supply curve, $q^s(p)$.
(c) Calculate the market equilibrium price $p^*$ and quantity $Q^*$. Calculate the output $q^*$ that each firm produces and a typical firm's profit level.
(d) The government imposes a tax of $$\$ 1$$ per manhole cover produced on each firm. What will be the long-run price $p_{l r}$ after entry or exit?
(e) If the tax remains in place, calculate the approximate number of firms in the long run (round down to the nearest integer).

Erwin Antoni

Numerade Educator

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Problem 3

In the market for a product, there are 100 identical competitive firms, each firm having the cost function $c(q)=200+0.5 q^2$, where $q$ is the quantity of output in tons produced by each firm. The market demand curve is given by $Q^d=3200-100 p$.
(a) Find the market equilibrium price $p^*$ and quantity produced by each firm, $q^*$.
(b) What will be the market equilibrium price in the long run, $p_{\text {lr }}$, after entry or exit? How many firms will there be after entry or exit?

Rashmi Sinha

Numerade Educator

04:56

Problem 4

In Takeout Town, there are 45 identical pizza delivery firms, each firm having the cost function $c(q)=0.5 q^2+4 q+162$, where $q$ is the quantity of pizzas produced by a typical firm. The market demand curve is given by $Q^d(p)=820-5 p$.
(a) Find a firm's individual supply curve $q^s(p)$ and the market supply curve $Q^S(p)$. Calculate the market equilibrium price $p^*$ and quantity $Q^*$. Calculate the firm output $q^*$ and profit level.
(b) What will be the long-run price $p_{l r}$ after entry or exit? Calculate the approximate number of firms in the long run (round down to the nearest integer).

Erwin Antoni

Numerade Educator

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Problem 5

In the market for a product, there are 100 identical competitive firms, each firm having the cost function $c(q)=0.5 q^2+5 q+50$, where $q$ is the quantity of output in tons produced by each firm. The market demand curve is given by $Q^d=1660-20 p$.
(a) Find the market equilibrium price $p^*$ and quantity produced by each firm, $q^*$.
(b) A permanent increase in demand shifts the market demand to $Q^d=1900-20 p$. What will be the approximate price $p^{* *}$ (up to two decimal places) in this market in the short run?
(c) Given the permanent increase in demand, how many firms will there be in this market in the long run after entry or exit?

Rashmi Sinha

Numerade Educator

03:48

Problem 6

In the market for soy beans, there are 520 identical farms, each farm having the cost function $c(q)=0.5 q^2+3 q+32$, where $q$ is the quantity of output in tons produced by each farm. The market demand curve is given by $Q^d(p)=4640-100 p$.
(a) Calculate the market equilibrium price $p^*$ and quantity $Q^*$. Calculate the output $q^*$ that each firm produces and the losses made by a typical farm.
(b) In view of the losses, the farmers wish to lobby the government for a price support program. What is the lowest support price acceptable to the farmers?

Niamat Khuda

Numerade Educator

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Problem 7

There are 40 identical firms that are perfectly competitive. The market demand is given by $Q^d(p)=2160-120 p$. The cost function for any firm is $c(q)=0.5 q^2+2 q+72$.
(a) Calculate the market equilibrium price and firm profits.
(b) An increase in property taxes raises each firm's fixed cost from $$\$ 72$$ to $$\$ 84.50$$. How many firms will there be after entry or exit in the long run?

Rashmi Sinha

Numerade Educator

07:01

Problem 8

There are many identical taxi drivers in a small town, each driver having the cost function $c(q)=128+4 q+0.5 q^2$, where $q$ is the number of passengers per day. The cost function includes a normal profit margin for the driver. The market demand is given by $Q^d=1680-4 p$.
(a) Calculate the long-run price for a ride in this market and the number of taxis in the long run.
(b) The city wants to control the number of taxis by requiring drivers to purchase a daily permit. They want the total number of taxis on any day to be $60 \mathrm{in}$ all. What is the maximum amount the city can charge from each driver for the permit? Explain!

Oluwadamilola Ameobi

Numerade Educator

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Problem 9

There are US cotton farmers and international (non-US) cotton farmers. All farmers are assumed to be perfectly competitive on the world market. The world demand for cotton is given by $Q^d(p)=12,000-100 p$.
(a) To begin with, assume that all farmers are identical and the cost function for any farmer, US or international, is given by $c(q)=$ $0.5 q^2+162$, where $q$ is the farmer's output. There are 300 US and 200 international farmers. Find a firm's individual supply curve $q^s(p)$ and the world market supply curve $Q^s(p)$ to calculate the world equilibrium price $p^*$.
(b) The US government decides to give a subsidy to the 300 US cotton farmers after which a US-farmer's cost function becomes $c_u\left(q_u\right)=$ $0.3 q_u^2+162$. The 200 international farmers have the same cost function as in (a). Assuming that the number of farmers does not change in the short run, find the new world supply $Q_n^s(p)$ and calculate the new world equilibrium price after this subsidy $p^{* *}$.
(c) Calculate the profits of US and international farmers at $p^{* *}$. What will happen to international farmers in the long run?
(d) Assume that the number of US farmers remains unchanged at 300 in the long run. Calculate the approximate number of international farmers that will be in the cotton market in the long run (round down to the nearest integer).

Lainey Roebuck

Numerade Educator