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1.(Capital and the Labour Market, Question with Mathematical) derivations). Consider our 4- quadrant model (for 1 sector only), take everything as standard there, but with the following particular specification : the production function is given by


Y= AKaL1-a , with 0 ≤a≤1


d.      Forget anything you have been told about the shape of the MPL as a function of L in class. Suppose in this sector, capital can be rented freely at r such that MPK= r . What does the four- quadrant equilibrium look like in this case? (It’s still the case that p1= MPL, and the MPL is a function of A, K, L).





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(Capital and the Labour Market, Question with Mathematical) derivations). Consider our 4- quadrant model (for 1 sector only), take everything as standard there, but with the following particular specification : the production function is given by


Y=AKaL1-a, with 0 ≤a≤1


a.      Show graphically the equilibrium in the labour market, taking A, K as fixed and given.

b.     Write down the key equation behind each quadrant.

c. Suppose an interest rate change has the following two effects: K goes down (less capital is used in production and the MPL in quadrant- I still takes this now-lower quantity of K as given) and β goes down. What happens to the equilibrium in the labour market, compared to (a)? (Illustrate graphically, if there any shift on the curve please explain). 







Discuss the effects of globalization on government spending anchored on the three theories presented by heimberger (2020).


Discuss the effects of global stratification on the philippine economy.


The distribution of marks scored by college students is shown below: Marks No. of students 0-20 45 20-30 21 30-50 15 50-60 10 60-90 5 90-100 2 i) Draw a histogram and comment on it's shape ii) Calculate the mean and median What proportion of students score less than 60 marks and what proportion scores between 50 to 80 marks.
Construct a box plot for the following data set. 3, 5, 8, 8, 9, 11, 12, 12, 13, 13, 16, 28 1. Find the range, inter-quartile range and skewness of the distribution? 2. Also identify outliers if any.

Discuss whether a government should increase or decrease taxes to reduce inflation


Problem 2: Consider the following production function: y=250K^{0.2}L^{0.8} . The wage rate is $24/hr, and the rental rate on capital is $2/hr. You must use calculus to solve this problem. Show and explain all work. A) Compute the cost minimizing combination of capital (K) and labor (L) required to produce 1000 units of output and then compute the minimum cost of producing this output. B) Draw and fully label a diagram showing the cost minimizing choice of K and L and the associated isoquant and isocost curve and explain your diagram fully. This includes: 1. Interpreting the slope of the isocost curve. 2. Labeling the intercepts of the isocost curve 3. Labeling the point on the isoquant curve showing the optimal combination of capital (K) and labor (L) 4. Labeling the level of output corresponding to the isoquant curve.

Ian Legon paid $100 deposit to Selene Robbins against purchase of her car on the understanding that Selene will keep the offer open for one month while Ian raises the rest of the money. Before the end of the month Selene accepts an ofer of more money for the car than she was originally asking. What is Ian's position? 


what is indifference curve explain with the help of diagram and also explain its properties