ECO $101$: Introduction to Microeconomics

Problem Set #$5$

Lectures $9$ & $10$

Due Date: $25$ November at $10$:$00$ pm

Total Points: $30$

Problem $1$: Perfect Competition & Long$-$Run Costs $[14$ Points$]$

Suppose that a firm has the following Long$-$Run Cost Curve:

This implies a MC of:

$TC=100+Q^2$

$MC=2Q$

This firm is part of a perfectly competitive market, made up of many identical firms.

The Demand in this market is: $Q=200-p$

Suppose that these firms begin in Long$-$Run Equilibrium.

What is this firm's Long$-$Run Average Total Costs $($LRAC$)$ as a function of $Q?[1$ point$]$

What quantity does each firm produce in Long$-$Run Equilibrium? $[3$ points$]$

How many firms exist in the market $(N)$ in the Long$-$Run? $[2$ points$]$

Draw what Long$-$Run Equilibrium looks like in this market with two figures. The first figure should have the Supply and Demand for the full market. The second figure has the individual cost curves, MC and LRAC, for this firm. Include the quantities produced on each. $[2$ points$]$

Now suppose that there is a decrease in this firms Cost function to now be equal to:

$TC=100+0\mathrm{.}5Q^2$

$MC=Q$

This implies a MC of:

$5.$ What happens to firm's prices and Long$-$Run profits in the Short$-$Run? Answer this drawing on your two figures from Q$4.$ You don't need to calculate the new numbers. $[3$ points$][$Note: You can calculate Long$-$Run profits using Long$-$Run costs, even in the Short$-$Run.$]$

$6.$ What will the new Long$-$Run price be$?$ What quantity will each firm produce in the Long$-$Run? How many firms will exist in the market in the Long$-$Run? $[3$ points$]$

$1$