The Saylor Foundation 1. Problem Set Unit 1 Answer Key. 1. Answer: In period 1,
we produced: Good. Price. Quantity. Total. X1. 5. X. 10. = 50. X2. 7. X. 14. = 98.
Problem Set Unit 1 Answer Key
1. Answer: In period 1, we produced: Good Price X1 5 X2 7 X3 6 X4 15
Good X1 X2 X3 X4
Good X1 X2 X3 X4
In period 2:
In period 3:
Price 5 7 6 15
Price 5 7 6 15
X X X X
X X X X
X X X X
Quantity Total 10 = 50 14 = 98 6 = 36 0 = 0 GDP = 184 Less 25 Consumption = 159 Quantity Total 10 = 50 14 = 98 6 = 36 4 = 60 GDP = 244 Less 25 Consumption = 219 Quantity Total 10 = 50 14 = 98 6 = 36 4 = 60 GDP = 244 Less 25 Consumption = 219
Total = 184+244+244= 672 Note: In period 1, production of X4 = 0 because the economy lacks X1 as an input. 2. Answer: Period 1: Period 2: Period 3:
159 x 1 = 159 244 x 1.05 = 256 244 x 1.05 x 1.08 = 277
The Saylor Foundation 1
Nominal GDP over the three periods is 184 + 256+ 277 =717 3. Answer: a) The rate of growth is the derivative of the function. b) f’(xt) = 3 xt2/2 The rate of change of growth is the double derivative. F’’(xt) = 3xt c) Output is highest at X2, or 10. d) At no time is the economy in recession since the rate of growth is always positive. 4. Answer for a, b, c:
F’(Xt) = -x2t + 1 = 0 X = +1 For values between +1, slope is positive (inflation). For Xt < -1 and Xt > 1, slope is negative (deflation). Answer for d: F’’(Xt) = -2Xt Only from time t = 0 to t = 1 is the first derivative increasing (inflation) and the second derivation decreasing (the rate of inflation is slowing).
