1. **Problem statement:** a) Deduce the budget equation for a housewife with 56 FCFA to spend on meat (X) and rice (Y), each costing 8 FCFA per kilogram. b) Derive the marginal utility (MU) schedules for meat (X) and rice (Y) from the total utility (TU) data. 2. **Budget equation:** The total money spent on meat and rice cannot exceed 56 FCFA. Let $x$ be kilograms of meat and $y$ be kilograms of rice. Price per kg of meat = 8 FCFA, price per kg of rice = 8 FCFA. Budget equation: $$8x + 8y = 56$$ Simplify by dividing both sides by 8: $$\cancel{8}x + \cancel{8}y = \cancel{8}7$$ $$x + y = 7$$ 3. **Marginal utility (MU) definition:** MU is the change in total utility when one more unit is consumed. 4. **Calculate MU for meat (X):** \[\text{MU}_X(n) = TU_X(n) - TU_X(n-1)\] For units 1 to 6: - MU_X(1) = 36 (since no previous unit) - MU_X(2) = 68 - 36 = 32 - MU_X(3) = 92 - 68 = 24 - MU_X(4) = 108 - 92 = 16 - MU_X(5) = 120 - 108 = 12 - MU_X(6) = 118 - 120 = -2 5. **Calculate MU for rice (Y):** - MU_Y(1) = 72 - MU_Y(2) = 132 - 72 = 60 - MU_Y(3) = 180 - 132 = 48 - MU_Y(4) = 204 - 180 = 24 - MU_Y(5) = 224 - 204 = 20 - MU_Y(6) = 232 - 224 = 8 --- 6. **Problem statement:** Fill the missing values in the cost table given fixed cost (FC), variable cost (VC), total cost (TC), average fixed cost (AFC), average variable cost (AVC), average total cost (ATC), and marginal cost (MC). 7. **Formulas:** - $TC = FC + VC$ - $AFC = \frac{FC}{Q}$ where $Q$ is output - $AVC = \frac{VC}{Q}$ - $ATC = \frac{TC}{Q} = AFC + AVC$ - $MC = \Delta TC / \Delta Q$ 8. **Calculate missing values:** | Output | FC | VC | TC = FC + VC | AFC = FC/Q | AVC = VC/Q | ATC = TC/Q | MC | |--------|-------|-------|-------------|------------|------------|------------|----| | 0 | 1080 | 0 | 1080 | - | - | - | - | | 1 | 1080 | 400 | 1080 + 400 = 1480 | 1080/1=1080 | 400/1=400 | 1480/1=1480 | 450 | | 2 | 1080 | 850 | 1080 + 850 = 1930 | 1080/2=540 | 850/2=425 | 1930/2=965 | 500 | | 3 | 1080 | 1350 | 1080 + 1350 = 2430 | 1080/3=360 | 1350/3=450 | 2430/3=810 | 550 | | 4 | 1080 | 1900 | 1080 + 1900 = 2980 | 1080/4=270 | 1900/4=475 | 2980/4=745 | MC(4) | 9. **Calculate missing MC at output 4:** $$MC(4) = TC(4) - TC(3) = 2980 - 2430 = 550$$ 10. **Calculate missing AVC at output 4:** $$AVC(4) = \frac{1900}{4} = 475$$ 11. **Summary of missing values:** - TC at outputs 1 to 4: 1480, 1930, 2430, 2980 - AFC at outputs 1 to 4: 1080, 540, 360, 270 - AVC at output 4: 475 - ATC at output 4: 745 - MC at output 4: 550 **Final answers:** - Budget equation: $$x + y = 7$$ - Marginal utilities: - Meat (X): 36, 32, 24, 16, 12, -2 - Rice (Y): 72, 60, 48, 24, 20, 8 - Completed cost table values as above.