# 3 tasks on statistics

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## Product description

Suppose that in the short run the firm can vary the use of labor resources, but can not affect the amount of capital employed. Table 1 shows how to change the output as a result of changes in the volume of labor employed.
Table 1
The costs of labor, L volume of production, Q MPL APL
+ 16 1 35
2 80 + 16
3122 + 16
4156 + 16
5177 + 16
6180 + 16
Required:
- To determine the marginal productivity of labor MPL and average productivity APL;
- Build curves MPL and APL, marked on the Ox axis - the number of labor costs and on the y-axis - limit (average) labor productivity;
- Determine at what amount of labor costs marginal and average productivity are the same;
- Think about how much work it is advisable to use the company.

Table 3 shows the data for the restructuring of production in the country in wartime.
TABLE 3
Combination Tractors Machine guns Opportunity costs
A 7 0
B 6 10 + 16
C 5 19 + 16
D April 27 + 16
E 3 34 + 16
F 2 40 + 16
G 1 45 + 16
H + 0 49 16
Required:
- A curve of production possibilities of the country, on the Ox axis shows the number of guns produced on the y-axis - the number of produced tractors;
- Define the maximum number of guns can be made;
- Determine what the optimum number of tractors can be made;
- Find the opportunity cost of producing one machine gun according to the table and fill the column №4, ie calculated from a number of tractors have to refuse to produce an additional quantity of machine guns.

Initial data for the calculation are given in Table 5.
Table 5
Number Demand for tickets to the theater notional price 1st ticket, standard units The proposed number of tickets to the theater coefficient of price elasticity tsprosa offers
1425 0.5 25
2 350 0.75 80
3295 1.0 135
4250 1.25 175
5215 + 16 + 16 215 1.5
6170 + 16 240 + 16 1.75
7115 2.0 275 + 16 + 16
8 16 2.25 70 + 310 + 16
9 45 + 16 + 16 325 2.5
Required:
- Find an equilibrium market price - the price of one ticket vteatr;
- To plot the supply and demand for tickets;
- To calculate the coefficient of price elasticity of demand and supply through the point elasticity formula, the calculation results are shown in Table 5;
- For what values \u200b\u200bthe price demand is elastic (inelastic);
- For what values \u200b\u200bthe offer price elastic (inelastic);
- To define the price range, which might reduce them to increase the number of ticket sales and overall revenue growth of the theater;
- Describe the consequences of centralized intervention in the market mechanism of price regulation: what happens if the state will set the price of 0,5 conv. units above or below the equilibrium value.