Answer to Question #315387 in Microeconomics for Axis

Question

1. Consider the market supply curve which passes through the intercept and from which the market equilibrium data is known, this is, the price and quantity of equilibrium 𝑷𝑬=𝟓𝟎 and 𝑸𝑬=𝟐𝟎𝟎𝟎.

a. Considering those two points, find the equation of the supply.

b. Draw a graph of this line.

2. Considering the previous supply line, determine if the following demand function corresponds to the market demand equilibrium stated above. 𝑸𝑫=𝟑𝟎𝟎𝟎−𝟐𝒑.

3. The production function of a firm is described by the following equation 𝑸=𝟏𝟎,𝟎𝟎𝟎𝑳−𝟑𝑳 𝟐 where L stands for the units of labor.

a) Draw a graph for this equation. Use the quantity produced in the y-axis and the units of labor in the x-axis.

b) What is the maximum production level?

c) How many units of labor are needed at that point?

4. Solve the following system of equations.

50𝑥+20𝑦=1800 10𝑥+3𝑦=300

Answer 1

The equation is (2000,50)

To find the slope we do as follows

$m = (0,0),(2000,50)$

$m= \frac{1}{40}$

$\frac{1}{40} = (2000,50), (Q,P)$

$40P -2000= Q-2000$

$P= \frac{Q}{40}$ or Q=40P

The above is the supply equation.

The graph of this line is as shown below

Considering the previous supply line;

$Q=4P$

To find equilibrium, we equate it to the given Qd.

$40P = 3000-2P$

$P= 71.42$

From this result the Qd does not correspond to the market equilibrium.

$50x+20y= 1800$

$10x+3y=300$

Solving the equations simultaneously

Multiply equation 2 by 5

$50x +20y = 1800$

$50x+ 15y = 1500$

$5y =300$

$y = 60$

Solving for x

$50x+1200 =1800$

$50x= 600$

$x = 12$