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

$50x+1200 =1800$

$50x= 600$

$x = 12$