Question

shangri - la produces only two goods: bats and balls. each worker comes with a fixed quantity of material and capital, and the economys labour force is fixed at 50 workers. the following table indicates the amounts of bats and balls that can be produced daily with various quantities of labour

number of workers	daily production of balls	number of workers	daily production of bats
10	90	10	29
20	150	20	52
30	195	30	67
40	225	40	76
50	240	50	80

a. complete the production possibilities in the table below.

	a	b	c	d	e	f
bats						0
bats 2						0

b. the opportunity cost of increasing the output of bats from 67 to 76 units per day is (click to select).

c. suppose that the planning office dictates an output of 150 balls and 82 bats per day. this output combination (click to select) possible.

d. now, assume that new technology is introduced in the production of bats so that each worker can produce half a bat more per day. complete the row bats 2, in the table in part (a) above, given this technological change.

e. the planning offices goal of 150 balls and 82 bats (click to select) be met

Explanation:

Step1: Fill Production Possibilities (Part a)

First, map workers to output:

• Point A: 0 balls → 50 workers on bats → 80 bats
• Point B: 90 balls (10 workers) → 40 workers on bats → 76 bats
• Point C: 150 balls (20 workers) → 30 workers on bats → 67 bats
• Point D: 195 balls (30 workers) → 20 workers on bats → 52 bats
• Point E: 225 balls (40 workers) → 10 workers on bats → 29 bats
• Point F: 240 balls (50 workers) → 0 bats

For Bats 2 (new tech): Each worker makes 0.5 more bats. New bat output = original + (workers × 0.5)

• Point A: 80 + (50×0.5) = 105 bats
• Point B: 76 + (40×0.5) = 96 bats
• Point C: 67 + (30×0.5) = 82 bats
• Point D: 52 + (20×0.5) = 62 bats
• Point E: 29 + (10×0.5) = 34 bats
• Point F: 0 + (0×0.5) = 0 bats

Step2: Calculate Opportunity Cost (Part b)

Increasing bats from 67 to 76: Shift from 30→40 workers on bats, so balls drop from 195 to 225? No, reverse: Bats 67 (30 workers) → 76 (40 workers): Balls go from 195 to 225? No, workers on balls go from 20→10, so balls drop from 195 to 90? No, correct: To get 9 more bats (76-67), we lose 225-195=30 balls. Opportunity cost = 30 balls.

Step3: Evaluate Output Feasibility (Part c)

150 balls needs 20 workers, leaving 30 workers for bats (max 67 bats). 82 bats > 67, so impossible.

Step4: Evaluate New Tech Feasibility (Part e)

150 balls needs 20 workers, leaving 30 workers for bats. New bat output for 30 workers: 67 + (30×0.5) = 82 bats, so feasible.

Answer:

Part a

	A	B	C	D	E	F
Bats	80	76	67	52	29	0
Bats 2	105	96	82	62	34	0

Part b

30 balls

Part c

impossible

Part e

can