1) Consider the production function given by Y = K1/3 x /2/3. Compute output when K = 27 and / = 8. If both capital and labor double, what happens to output? Is this production function characterized by constant returns to scale? Write this production function as a relation between output per worker and capital per worker. Let K/N = 8. What is Y/N?2) First, suppose the United States economy is represented by the following equations: Z =C+I+G, C=300 + .5Yp, YD=Y-T T = 400, / = 250, G = 1000 Given the above variables, calculate the equilibrium level of output. Now assume that consumer confidence increases causing a rise in autonomous consumption (c) from 300 to 500. What is the new equilibrium level of output? How much does income change as a result of this event? What is the multiplier for this economy? Please show your calculation details.3) Fill in the missing values in the following table. Assume that the value of the marginal propensity to consume does not change as real GDP changes and that there are zero taxes. Show your calculation details. (Enter all values as integers.) Y C H G NX AE $800 $500 $80 $120 -$10 $900 $560 $80 $120 -$10 $1.100 $80 $120 -$10 $1.300 $80 $120 $10 $1,500 $80 $120 -$10