Skip to main content

Exercise: Table of Production

You are given the following table of production, fill in the blank. Then graph the total product, average product and marginal product curves with respect to labor.
Labor (L)  Capital (k)  Output (Q)  Average Product (Q/L)   Marginal Product
4 3 51 ... n.a
5 3 ... 12.4 ...
6 3 ... ... 7
7 3 ... ... 2
8 3 ... 8.75 ...

The solution is:
Labor (L)  Capital (k)  Output (Q)  Average Product (Q/L)   Marginal Product
4 3 51 (51/4) n.a
5 3 62 (62/5) 11
6 3 69 (69/6) 7
7 3 71 (71/7) 2
8 3 70 (70/8) -1

If you know the average output and the number of workers (labor) then you know the output at each level (recall the formula for AP). If you know the marginal product for a given number of workers, and if you know the previous total output for one less worker then you can find the total output for the given number of workers:



Let's graph the total product curve as a function of labor input:
Just by looking at this graph, one can observe that the slope (the rate of growth) of the total product curve is becoming smaller and smaller as the number of workers increases.

 Let's graph the APL (average product of labor) and MPL (marginal product of labor) curves as functions of labor input:

We can see that since the APL curve is decreasing, the MPL (marginal product of labor) must be below. Furthermore, as the number of workers increases from 4 to 7, the production experiences diminishing returns, the production increases at a decreasing rate as new workers are added. Finally when a 8th worker is added to the production line, we see that the firm is facing decreasing returns, the firm produces less than it would have without the additional worker. 


One easy way to find the marginal product of x (where x can be labor, capital, etc..) is by simply taking the partial derivative of a production function with respect to x. In other words:



The production function is represented by f(x,y,k) this means that the production function f depends on three different inputs or variables, namely x, y, and k (but it can depend on more or less variables). We take the derivative with respect to x, so we treat the other variables as constant. This gives us a general formula for the MP of x for this specific production function. Then, all we need to do is to plug into the derivative the different values of x,y,k (if possible, the derivative could just be a constant). 
Labels:

Comments

Post a Comment

Popular posts from this blog

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever   any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP).  Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest ...
Post a Comment
Read more

Exercise: inflation and GDP deflator

You have the following table containing information about country Y's GDP deflator, nominal, and real GDP. If the base year is 2015, fill in the blanks and then find the annual inflation rate for each year. Year  Nominal GDP  GDP Deflator  Real GDP 2015 $23,457 100 $23,457 2016 $25,752 ... $23,943 2017 $25,982 108.1 ... 2018 $26,016 ... $25,431.1 2019 $26,323 105.5 ... Solution: Year  Nominal GDP  GDP Deflator  Real GDP   Inflation rate 2015 $23,457 100 $23,457 n.a 2016 $25,752 107.6 $23,943 7.6% 2017 $25,982 108.1 $24,035.2 0.45% 2018 $26,016 102.3 $25,431.1 -5.37% 2019 $26,323 105.5 $24,950.6 3.13%  GDP deflator for the year 2018: Real GDP for the year 2017: General formula to find real GDP by re-arranging the GDP deflator formula: Notice that the sub-index i is for the year. The (annual) inflation rate is simply the growth rate of prices from a year to its previous year: Inflation rate of the year 2018: Notice that in 2018 country Y experienced...
Post a Comment
Read more

Exercise: Payoff matrix -Oligopoly market-

You are given a payoff matrix for two firms in an oligopoly market. Find the dominant strategy (if any) for each firm. What profit would they each earn if they form a cartel (if possible)? Can the cartel hold in the long run? If not, what is the long run equilibrium? Payoff Matrix:  Firm A: high prices  Firm A: low prices Firm B: high prices A: $1000 B: $1000 A: $1200 B: $800 Firm B: low prices A: $600 B: $1200 A: $700 B: $700 The dominant strategy for firm A is to charge a low price for its product. You can see that no matter what firm B chooses, firm A is always better off by choosing the low price option (i.e its profit is always bigger than if it had charged a high price). The strategy for firm B depends on the choices firm A makes. If firm A charges a high (low) price then firm B should charge a low (high) price. In order to find the point at which the firms would collude (i.e act as one monopolistic firm), find the point(s) where the sum of economic profits is the greate...
Post a Comment
Read more