Question #315387

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=πŸ“πŸŽ 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=πŸ‘πŸŽπŸŽπŸŽβˆ’πŸπ’‘.


3. The production function of a firm is described by the following equation 𝑸=𝟏𝟎,πŸŽπŸŽπŸŽπ‘³βˆ’πŸ‘π‘³ 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.

50π‘₯+20𝑦=1800 10π‘₯+3𝑦=300




1
Expert's answer
2022-03-22T19:05:15-0400

The equation is (2000,50)

To find the slope we do as follows

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

m=140m= \frac{1}{40}

140=(2000,50),(Q,P)\frac{1}{40} = (2000,50), (Q,P)

40Pβˆ’2000=Qβˆ’200040P -2000= Q-2000

P=Q40P= \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=4PQ=4P


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

40P=3000βˆ’2P40P = 3000-2P

P=71.42P= 71.42

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


50x+20y=180050x+20y= 1800

10x+3y=30010x+3y=300

Solving the equations simultaneously

Multiply equation 2 by 5

50x+20y=180050x +20y = 1800

50x+15y=150050x+ 15y = 1500

5y=3005y =300

y=60y = 60

Solving for x

50x+1200=180050x+1200 =1800

50x=60050x= 600

x=12x = 12


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