Economics of Enterprise Answers

Problem 1 Let X 1 , X 2 , ⋯,Xn be a random sample from a normal distribution with mean µ and variance σ 2 . Consider e X as an estimator of e µ where X is the sample mean. Show that e is consistent estimator of e µ X .

Problem 1 Let X 1 , X 2 , ⋯,Xn be a random sample from a normal distribution with mean µ and variance σ 2 . Consider e X as an estimator of e µ where X is the sample mean. Show that e is consistent estimator of e µ X .

A random sampleY1 , Y 2 , ⋯,Yn is drawn from a distribution whose probability density function is given by: f (Y ) = βe − βY , Y  0 & β > 0 a). Obtain the maximum likelihood estimator (MLE) of β. (3 points) 1Econometrics- Assignment I b). Given that ∑ n Y i = 25 , ∑n Yi 2 = 50 , n = 50 calculate the maximum likelihood i =1 i =1 estimate of β. (3 point) c). Using the same data as in part (b), test the null hypothesis that β =1against the alternative hypothesis that β ≠1at 5% level of significance. (3 points) Problem 4 Suppose the production(Y) is determined as a function of labour input in hours (L) and capital input in machine hours (K). Using the Cobb-Douglas function

How will the COVID-19 pandemic crisis affect the natural rate of unemployment? Explain the reasoning behind your answer.

. Demand Curves. ISHO-garment is contemplating a T-shirt advertising promotion. Monthly sales data from T-shirt shops marketing indicate that

            𝑄=1,500–200𝑃

1.   The countries France and Italy produce Perfumes and Leather Coats using only labor as an input. AvailableLabor for France and Italy is 3000 and 1000 respectively. Unit of labor per Leather Coat in France is 6 units and inItaly are 2 units. France needs 2 units of labors to produce 1 bottle of Perfume and Italy needs 4 unit of labor.

a)  Draw the Production Possibility Curve by using relevant information. (1*2=2 marks)

b)  Which country has the comparative advantage in producing Perfume? (3 marks)

From the give table calculate Elasticity of Price, Total Revenue and Marginal Revenue.

Also, explain the relationship between AR and MR?

Show that the test taking the overall significance of regression model using ANOVA table to be expressed as: 

𝑹𝟐⁄𝒌−𝟏

𝑭=(𝟏−𝑹𝟐)⁄𝒏−𝒌 

Where, R be a level of determination and k is the number of parameters in the n sampled regression model.

Consider a k-variables linear regression model, i.e.,

Y = X 1β1 + X 2 β2 + ε,

Where, X1 is (N  k1 ) , X 2 is (N  k2 ) and k = k1 + k2 . As you may recall, adding columns to the X matrix (including additional regressors in the model) gives positive definite increase in R2. The adjusted R2 ( R 2 ) attempts to avoid this phenomenon of ever increase in R2. Show that the additional k2 number of variables (regressors) in this model increases R 2 if the calculated F-statistic in testing the joint statistical significance of coefficients of these additional

regressors (β2 ) is larger than one.

a firm’s demand curve in period 1 is q=25 - p. fixed costs are 20 and marginal costs per unit are 5

At what output will marginal revenue be zero?

At what price will total revenue be maximized? 

At what price and output will profit be maximized?

Calculate the maximum profits the firm makes